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Artykuły w czasopismach na temat „Interpolation”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Earshia V., Diana, and Sumathi M. "Interpolation of Low-Resolution Images for Improved Accuracy Using an ANN Quadratic Interpolator." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 4s (2023): 135–40. http://dx.doi.org/10.17762/ijritcc.v11i4s.6319.

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The era of digital imaging has transitioned into a new one. Conversion to real-time, high-resolution images is considered vital. Interpolation is employed in order to increase the number of pixels per image, thereby enhancing spatial resolution. Interpolation's real advantage is that it can be deployed on user end devices. Despite raising the number of pixels per inch to enhances the spatial resolution, it may not improve the image's clarity, hence diminishing its quality. This strategy is designed to increase image quality by enhancing image sharpness and spatial resolution simultaneously. Pr

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2

Gashnikov, M. V. "Parameterized interpolation for fusion of multidimensional signals of various resolutions." Computer Optics 44, no. 3 (2020): 436–40. http://dx.doi.org/10.18287/2412-6179-co-696.

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Parameterized interpolation algorithms are adapted to fusion of multidimensional signals of various resolutions. Interpolating functions, switching rules for them and local features are specified, based on which the interpolating function is selected at each point of the signal. Parameterized interpolation algorithms are optimized based on minimizing the interpolation error. The recurrent interpolator optimization scheme is considered for the situation of inaccessibility of interpolated samples at the stage of setting up the interpolation procedure. Computational experiments are carried out to

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3

Xu, Weizhi. "Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique." Statistics, Optimization & Information Computing 8, no. 4 (2020): 994–1010. http://dx.doi.org/10.19139/soic-2310-5070-1083.

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This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic

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4

Parker, Joshua, Dionne Ibarra, and David Ober. "Logarithm-Based Methods for Interpolating Quaternion Time Series." Mathematics 11, no. 5 (2023): 1131. http://dx.doi.org/10.3390/math11051131.

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In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables θ and n^ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quate

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5

Etherington, Thomas R. "Discrete natural neighbour interpolation with uncertainty using cross-validation error-distance fields." PeerJ Computer Science 6 (July 13, 2020): e282. http://dx.doi.org/10.7717/peerj-cs.282.

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Interpolation techniques provide a method to convert point data of a geographic phenomenon into a continuous field estimate of that phenomenon, and have become a fundamental geocomputational technique of spatial and geographical analysts. Natural neighbour interpolation is one method of interpolation that has several useful properties: it is an exact interpolator, it creates a smooth surface free of any discontinuities, it is a local method, is spatially adaptive, requires no statistical assumptions, can be applied to small datasets, and is parameter free. However, as with any interpolation me

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6

Gashnikov, M. V. "Interpolation based on context modeling for hierarchical compression of multidimensional signals." Computer Optics 42, no. 3 (2018): 468–75. http://dx.doi.org/10.18287/2412-6179-2018-42-3-468-475.

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Context algorithms for interpolation of multidimensional signals in the compression problem are researched. A hierarchical compression method for arbitrary dimension signals is considered. For this method, an interpolation algorithm based on the context modeling is proposed. The algorithm is based on optimizing parameters of the interpolating function in a local neighborhood of the interpolated sample. At the same time, locally optimal parameters found for more decimated scale signal levels are used to interpolate samples of less decimated scale signal levels. The context interpolation algorit

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7

Richard, William D., and R. Martin Arthur. "Real-Time Ultrasonic Scan Conversion via Linear Interpolation of Oversampled Vectors." Ultrasonic Imaging 16, no. 2 (1994): 109–23. http://dx.doi.org/10.1177/016173469401600204.

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Scan conversion is required in order to display conventional B-mode ultrasonic signals, which are acquired along radii at varying angles, on standard Cartesian-coordinate video monitors. For real-time implementations, either nearest-neighbor or bilinear interpolation is usually used in scan conversion. If the sampling rate along each radius is high enough, however, the gray-scale value of a given pixel can be interpolated accurately using the nearest samples on two adjacent vectors. The required interpolation then reduces to linear interpolation. Oversampling by a factor of 2 along with linear

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8

Arana, Daniel, Fabricio dos Santos Prol, Paulo de Oliveira Camargo, and Gabriel do Nascimento Guimarães. "ERRORS MEASUREMENT OF INTERPOLATION METHODS FOR GEOID MODELS: STUDY CASE IN THE BRAZILIAN REGION." Boletim de Ciências Geodésicas 24, no. 1 (2018): 44–57. http://dx.doi.org/10.1590/s1982-21702018000100004.

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Abstract: The geoid is an equipotential surface regarded as the altimetric reference for geodetic surveys and it therefore, has several practical applications for engineers. In recent decades the geodetic community has concentrated efforts on the development of highly accurate geoid models through modern techniques. These models are supplied through regular grids which users need to make interpolations. Yet, little information can be obtained regarding the most appropriate interpolation method to extract information from the regular grid of geoidal models. The use of an interpolator that does

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9

Shen, Hai Ming, Kun Qi Wang, and Yong You Tian. "Design of Interpolation Algorithm in the Multi-Axis Motion Control System." Advanced Materials Research 411 (November 2011): 259–63. http://dx.doi.org/10.4028/www.scientific.net/amr.411.259.

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This paper describes an interpolation algorithm in the multi-axis motion control system, which can achieve six-axis interpolation operations, greatly improving the processing efficiency. Using modular design idea on the Quartus II platform, by DDA interpolation theory, interpolation modules are built through VHDL. And these interpolator modules are connected into schematic diagrams. By those schematic diagrams a linear interpolator, a circular interpolator and a composite interpolator are formed. The corresponding functions of those interpolators have been simulated on the Quartus II platform.

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10

Barker, Paul M., and Trevor J. McDougall. "Two Interpolation Methods Using Multiply-Rotated Piecewise Cubic Hermite Interpolating Polynomials." Journal of Atmospheric and Oceanic Technology 37, no. 4 (2020): 605–19. http://dx.doi.org/10.1175/jtech-d-19-0211.1.

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AbstractTwo interpolation methods are presented, both of which use multiple Piecewise Cubic Hermite Interpolating Polynomials (PCHIPs). The first method is based on performing 16 PCHIPs on 8 rotated versions of the plot of the data versus an independent variable (such as pressure or time). These 16 PCHIPs are then used to form 8 interpolations of the original data, and finally, these 8 are averaged. When the original data are unevenly spaced with respect to the independent variable, we show that it is best to perform the Multiply-Rotated PCHIP (MR-PCHIP) method using the “data index” as the in

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11

Guo, Jing Jie, and Wei Tang. "Design of Pythagorean Hodograph Curve Interpolator Based on NiosII Embedded Processor and FPGA." Advanced Materials Research 383-390 (November 2011): 6868–72. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.6868.

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In this paper, a novel architecture of Pythagorean Hodograph (PH) curve interpolator based on Nios Ⅱ embedded processor and FPGA is proposed. The whole interpolator including NiosⅡ processor is built in a single FPGA chip. The interpolator uses a two-stage interpolation scheme to reduce the computational burden of PH curve interpolator. The Nios Ⅱ embedded processor implements 1st-stage interpolation, the FPGA receives the command from the Nios Ⅱ processor and implements 2nd-stage interpolation simultaneously. Therefore, the interpolator can implement the real-time PH curve interpolation algor

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12

Xie, S. H., Qiu Liao, and S. R. Qin. "Sub-Pixel Edge Detection for Precision Measurement Based on Canny Criteria." Key Engineering Materials 295-296 (October 2005): 711–16. http://dx.doi.org/10.4028/www.scientific.net/kem.295-296.711.

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A new nonlinear intensity interpolation algorithm is presented to realize sub-pixel edge detection. The interpolation algorithm based on the Canny criteria makes full use of grads information attained by Canny edge detection to perform special interpolation in the grads direction. When the resolution is enhanced, the interpolated image by the new interpolation scheme can efficiently preserve high frequency component in the original image. The edge detection of interpolated image permits high precision localization. The new interpolation algorithm is more effective in reserving the grads inform

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13

Fan, Xi Ying, Yong Huan Guo, Shun Cai Li, and Xiu Ping Su. "New Digital Differential Analyzer Linear Interpolation Program and Error Analysis." Advanced Materials Research 314-316 (August 2011): 1769–72. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.1769.

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Common digital differential analyzer（DDA）linear interpolation error is lower than a pulse equivalent, and the output pulse along each axis is not uniform. New DDA linear interpolation flow chart was obtained by combining a quick algorithm of DDA interpolation and interpolating algorithm for pulses uniformization with common DDA linear interpolation principle. The relationship between interpolation error and pulse equivalent was demonstrated in detail. As the results shows, the new DDA with high precision machining but simple algorithm, increased interpolating speed; the new algorithm make the

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14

Lho, T.-J., and S.-J. Na. "A Study on an Improved Direct Search Interpolation Method for Two-Axis CNC Thermal Cutting Systems." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 206, no. 1 (1992): 67–76. http://dx.doi.org/10.1243/pime_proc_1992_206_057_02.

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A microcomputer-based reference pulse software interpolator, which can be effectively applied for two-axis computer numerical control (CNC) systems such as those used in plasma arc cutting and laser beam cutting machines, is proposed in the present study. The proposed interpolation method is based upon searching in two or three directions for the minimum path error, while the axes of motion do not move simultaneously in the stairs approximation method and the basis for selecting an interpolating point is not related to any criteria of path error in the digital differential analyses (DDA) metho

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15

Essanhaji, A., and M. Errachid. "Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach." Journal of Applied Mathematics 2022 (March 14, 2022): 1–8. http://dx.doi.org/10.1155/2022/8227086.

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The problems of polynomial interpolation with several variables present more difficulties than those of one-dimensional interpolation. The first problem is to study the regularity of the interpolation schemes. In fact, it is well-known that, in contrast to the univariate case, there is no universal space of polynomials which admits unique Lagrange interpolation for all point sets of a given cardinality, and so the interpolation space will depend on the set Z of interpolation points. Techniques of univariate Newton interpolating polynomials are extended to multivariate data points by different

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16

Charnsamorn, Chapkit, and Suphongsa Khetkeeree. "Symmetric quadratic tetration interpolation using forward and backward operation combination." International Journal of Electrical and Computer Engineering (IJECE) 12, no. 2 (2022): 1893. http://dx.doi.org/10.11591/ijece.v12i2.pp1893-1903.

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The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several r

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17

Chapkit, Charnsamorn, and Khetkeeree Suphongsa. "Symmetric quadratic tetration interpolation using forward and backward operation combination." International Journal of Electrical and Computer Engineering (IJECE) 12, no. 2 (2022): 1893–903. https://doi.org/10.11591/ijece.v12i2.pp1893-1903.

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The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several r

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18

Flannigan, M. D., and B. M. Wotton. "A study of interpolation methods for forest fire danger rating in Canada." Canadian Journal of Forest Research 19, no. 8 (1989): 1059–66. http://dx.doi.org/10.1139/x89-161.

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Canadian fire control agencies use either simple interpolation methods or none at all in estimating fire danger between weather stations. We compare several methods of interpolation and use the fire weather index in the North Central Region of Ontario as a case study. Our work shows that the second order least square polynomial, the smoothed cubic spline, and the weighted interpolations had the lowest residual sum of squares in our verification scheme. These methods fit the observed data at both high and low fire weather index values. The highly variable nature of the spatial distribution of s

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19

Wang, Ren-Hong, and Jing-Xin Wang. "Quasi-interpolations with interpolation property." Journal of Computational and Applied Mathematics 163, no. 1 (2004): 253–57. http://dx.doi.org/10.1016/j.cam.2003.08.070.

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20

Gashnikov, M. V. "Interpolation of multidimensional signals using the reduction of the dimension of parametric spaces of decision rules." Information Technology and Nanotechnology, no. 2391 (2019): 31–40. http://dx.doi.org/10.18287/1613-0073-2019-2391-31-40.

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In this paper, we consider the interpolation of multidimensional signals problem. We develop adaptive interpolators that select the most appropriate interpolating function at each signal point. Parameterized decision rule selects the interpolating function based on local features at each signal point. We optimize the adaptive interpolator in the parameter space of this decision rule. For solving this optimization problem, we reduce the dimension of the parametric space of the decision rule. Dimension reduction is based on the parameterization of the ratio between local differences at each sign

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21

Wang, Jianmin, Yabo Li, Huizhong Zhu, and Tianming Ma. "Interpolation Method Research and Precision Analysis of GPS Satellite Position." Journal of Systems Science and Information 6, no. 3 (2018): 277–88. http://dx.doi.org/10.21078/jssi-2018-277-12.

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Abstract According to the precise ephemeris has only provided satellite position that is discrete not any time, so propose that make use of interpolation method to calculate satellite position at any time. The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation, Newton interpolation, Hermite interpolation, Cubic spline interpolation method, Chebyshev fitting method respectively, which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method

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22

Amar, Eric. "On interpolation of interpolating sequences." Indagationes Mathematicae 18, no. 2 (2007): 177–87. http://dx.doi.org/10.1016/s0019-3577(07)00011-0.

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23

Maksimov, A. I., and M. V. Gashnikov. "Parameter space dimension reduction of an adaptive interpolator during multidimensional signal differential compression." Information Technology and Nanotechnology, no. 2391 (2019): 23–30. http://dx.doi.org/10.18287/1613-0073-2019-2391-23-30.

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We propose a new adaptive multidimensional signal interpolator for differential compression tasks. To increase the efficiency of interpolation, we optimize its parameters space by the minimum absolute interpolation error criterion. To reduce the complexity of interpolation optimization, we reduce the dimension of its parameter range. The correspondence between signal samples in a local neighbourhood is parameterized. Besides, we compare several methods for such parameterization. The developed adaptive interpolator is embedded in the differential compression method. Computational experiments on

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24

Poghosyan, Arnak. "On a Fast Convergence of the Rational-Trigonometric-Polynomial Interpolation." Advances in Numerical Analysis 2013 (March 21, 2013): 1–13. http://dx.doi.org/10.1155/2013/315748.

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We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate convergence of the resultant parametric rational-trigonometric-polynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rational-trigonometric-polynomial interpolation compared to the Krylov-Lanczos interpolation is observed. Results of numerical experiments confirm theoretical estimates and show how the parameters of the interpolations can be determined in practice.

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25

Liang, Chang Chun, Liu Qun Fan, Dang Jin Qi, Gang Yi, and Zhuang Miao. "Optimal Interpolation Algorithm Research Based on Quasi-Hermite Space Curve." Advanced Materials Research 317-319 (August 2011): 215–21. http://dx.doi.org/10.4028/www.scientific.net/amr.317-319.215.

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According to the principle of parametric curve paths CNC interpolating, a real-time interpolation algorithm based on algebraic index of the micro-segment spline is presented. It’s used to solve the problems of Hermite polynomial interpolation algorithm, which are commonly slow recursive algorithm, poor accuracy of approximation and the limitations of constant parameters increment interpolation. And the constant interpolation is achieved by fitting a first-order Taylor Formula. Simulation results show that the algorithm shortens the interpolation time and also improve the interpolation accuracy

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26

Zou, You-Yun, Yu-Cheng Tian, D. M. Li, Xu-Bao Luo, and Bin Liu. "On Interpolative Meshless Analysis of Orthotropic Elasticity." Buildings 13, no. 2 (2023): 387. http://dx.doi.org/10.3390/buildings13020387.

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As one possible alternative to the finite element method, the interpolation characteristic is a key property that meshless shape functions aspire to. Meanwhile, the interpolation meshless method can directly impose essential boundary conditions, which is undoubtedly an advantage over other meshless methods. In this paper, the establishment, implementation, and horizontal comparison of interpolative meshless analyses of orthotropic elasticity were studied. In addition, the radial point interpolation method, the improved interpolative element-free Galerkin method and the interpolative element-fr

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27

Aziz, Siti Hawa. "Polynomial Interpolation in Matlab." Journal of Engineering and Science Research 2, no. 4 (2018): 12–19. http://dx.doi.org/10.26666/rmp.jesr.2018.4.3.

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The problem of constructing such a continuous function is called data fitting. Many times, data given only at discrete points. With interpolation, we seek a function that allows us to approximate f(x) such that functional values between the original data set values may be determined. The process of finding such a polynomial is called interpolation and one of the most important approaches used are Lagrange interpolating formula. In this study, researcher determining the polynomial interpolation by using Lagrange interpolating formula. Then, a mathematical modelling was built by using MATLAB pro

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Feng, Zhigang, and Heping Xie. "On Stability of Fractal Interpolation." Fractals 06, no. 03 (1998): 269–73. http://dx.doi.org/10.1142/s0218348x98000316.

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In this paper, a special kind of FIF (fractal interpolation function) is studied. The authors prove the stability of the fractal interpolations. When the interpolation data have a small perturbation, the corresponding FIFs also have a small perturbation.

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DeGaetano, Arthur T., Brian N. Belcher, and William Noon. "Temporal and Spatial Interpolation of the Standardized Precipitation Index for Computational Efficiency in the Dynamic Drought Index Tool." Journal of Applied Meteorology and Climatology 54, no. 4 (2015): 795–810. http://dx.doi.org/10.1175/jamc-d-14-0088.1.

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AbstractThe feasibility of interpolating gamma-distribution parameters between different precipitation accumulation intervals (durations) is statistically evaluated. The interpolation of these parameters for a specific accumulation interval, but ending on different dates, is similarly assessed. Such interpolation increases the computational efficiency of drought-monitoring tools that require calculation of the standardized precipitation index (SPI) for any user-specified accumulation period on any given day. Spatial interpolation of the distribution parameters is also assessed. Given a 60-yr p

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Kiani, M. "Spherical approximating and interpolating moving least squares in geodesy and geophysics: a case study for deriving gravity acceleration at sea surface in the Persian Gulf." Journal of Geodetic Science 10, no. 1 (2020): 124–35. http://dx.doi.org/10.1515/jogs-2020-0112.

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Abstract This paper is aimed at introducing the concept of Spherical Interpolating Moving Least Squares to the problems in geodesy and geophysics. Based on two previously known methods, namely Spherical Moving Least Squares and Interpolating Moving Least Squares, a simple theory is formulated for using Spherical Moving Least Squares as an interpolant. As an application, a case study is presented in which gravity accelerations at sea surface in the Persian Gulf are derived, using both the approximation and interpolation mode of the Spherical Moving Least Squares. The roles of the various elemen

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Chen, Hao, You Peng You, Jun He, and Xue Feng Yang. "A Separated-Axis Interpolator with Variable Period for Stepping Systems." Key Engineering Materials 431-432 (March 2010): 61–64. http://dx.doi.org/10.4028/www.scientific.net/kem.431-432.61.

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In motion systems driven by stepping motors, reference word interpolation is usually used with a constant period T, in which the existing position quantization errors will inevitably result in the trouble of velocity quantization errors. A separated-axis interpolator with variable period is proposed to deal with these troubles. The reassignment module of displacement and time is the key of the interpolator. In the module, the interpolation period of each axis can be separately adjusted upon its quantized displacement, thus resulting in almost ideal velocity profile and moving smoothness. Simul

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Jiang, Hong Fei. "Triangle Interpolation on Discrete Point Set." Applied Mechanics and Materials 580-583 (July 2014): 2872–75. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2872.

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An algorithm for triangle interpolation on discrete points is presented in the paper. It creates a square mesh which covers all the discrete points, then puts the points into the mesh and records the relationship between grids and points. When interpolating elevation of an interpolation point, it can fast find the discrete points which are near the interpolation point and these discrete points can be used to create a special triangle which contains the interpolation point. The elevation of the interpolation point can be obtained from the triangle. The method has the advantage of fast speed, hi

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Zhu, Li Da, Gang Li, and Wan Shan Wang. "Research on Interpolation Algorithm of Three-Links Hybrid Machine Tool." Advanced Materials Research 97-101 (March 2010): 3124–27. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.3124.

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Aiming at the characteristics of structure and control of three-links hybrid machine tool, the interpolation strategy of CNC system is proposed in this paper. Coarse interpolation in workspace and fine interpolation in joint-space are expatiated. The trajectory points are transformed into discrete points by coarse interpolation mapping from workspace to joint-space. At the same time, the plans of trajectory, velocity and acceleration of discrete points in workspace are got, and then joint discrete points are realized by joint fitting smooth function. In order to meet the design demand and enha

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You, You Peng, and Jun He. "A Parametric Interpolator with Smooth Kinematic Profiles for High Speed Machining." Key Engineering Materials 315-316 (July 2006): 169–73. http://dx.doi.org/10.4028/www.scientific.net/kem.315-316.169.

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Smooth kinematic profiles are very important for high speed curve machining. During parametric interpolation, simple adaptive feedrate with confined contour error may cause acceleration and jerk to fluctuate acutely. To avoid the undesirable influence, an interpolation algorithm for parametric curves with smooth kinematic profiles is presented. The interpolator consists of three parts, look-ahead module, feedrate planning module and interpolation module. In look-ahead module, a pre-interpolator is designed to produce the required feedrate profile considering chord error. By feedrate planning,

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Bau, David, Hendrik Himmelein, and Christoph Pörschmann. "Comparison of Non-Parametric Interpolation Techniques for Sparsely Measured Binaural Room Impulse Responses." Journal of the Audio Engineering Society 72, no. 7/8 (2024): 479–92. http://dx.doi.org/10.17743/jaes.2022.0150.

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This study investigates different interpolation techniques for spatially upsampling Binaural Room Impulse Responses (BRIRs) measured on a sparse grid of view orientations. In this context, the authors recently presented the Spherical Array Interpolation by Time Alignment (SARITA) method for interpolating spherical microphone array signals with a limited number of microphones, which is adapted for the spatial upsampling of sparse BRIR datasets in the present work. SARITA is compared with two existing nonparametric BRIR-interpolation methods and naive linear interpolation. The study provides a t

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Zhu, Dantong, Zhenhao Zhong, Minghao Zhang, et al. "An Improved Principal Component Analysis Method for the Interpolation of Missing Data in GNSS-Derived PWV Time Series." Remote Sensing 15, no. 21 (2023): 5153. http://dx.doi.org/10.3390/rs15215153.

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Missing data in precipitable water vapor derived from global navigation satellite systems (GNSS-PWV) is commonly a large hurdle in climatical applications, since continuous PWV is an important prerequisite. Interpolation using principal component analysis (PCA) is typically used to resolve this problem. However, the popular PCA-based interpolating methods, e.g., rank-deficient least squares PCA (RDPCA) and data interpolating empirical orthogonal function (DINEOF), often lead to unsatisfactory results. This study analyzes the relationship between missing data and PCA-based interpolation results

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Zou, Le, Liangtu Song, Xiaofeng Wang, Thomas Weise, Yanping Chen, and Chen Zhang. "A New Approach to Newton-Type Polynomial Interpolation with Parameters." Mathematical Problems in Engineering 2020 (November 16, 2020): 1–15. http://dx.doi.org/10.1155/2020/9020541.

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Newton’s interpolation is a classical polynomial interpolation approach and plays a significant role in numerical analysis and image processing. The interpolation function of most classical approaches is unique to the given data. In this paper, univariate and bivariate parameterized Newton-type polynomial interpolation methods are introduced. In order to express the divided differences tables neatly, the multiplicity of the points can be adjusted by introducing new parameters. Our new polynomial interpolation can be constructed only based on divided differences with one or multiple parameters

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WANG, HAO, WEI ZHANG, and YANYAN LIU. "NOVEL PIPELINED INTERPOLATOR FOR REED–SOLOMON DECODER BASED ON LOW-COMPLEXITY CHASE DECODING." Journal of Circuits, Systems and Computers 22, no. 10 (2013): 1340037. http://dx.doi.org/10.1142/s0218126613400379.

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Reed–Solomon (RS) codes are widely used in digital communication and storage systems. Algebraic soft-decision (ASD) decoding of RS codes can obtain significant coding gain over hard-decision decoding. Compared with other ASD algorithms, the low-complexity chase (LCC) decoding algorithm needs less computation complexity with similar or better coding gain. To reduce the latency of the interpolation, multiple interpolators can be applied. However, the interpolator has to finish the forward interpolation (FI) which costs more iterations before it turns to the unified-backward–forward interpolator

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Caloiero, Tommaso, Gaetano Pellicone, Giuseppe Modica, and Ilaria Guagliardi. "Comparative Analysis of Different Spatial Interpolation Methods Applied to Monthly Rainfall as Support for Landscape Management." Applied Sciences 11, no. 20 (2021): 9566. http://dx.doi.org/10.3390/app11209566.

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Landscape management requires spatially interpolated data, whose outcomes are strictly related to models and geostatistical parameters adopted. This paper aimed to implement and compare different spatial interpolation algorithms, both geostatistical and deterministic, of rainfall data in New Zealand. The spatial interpolation techniques used to produce finer-scale monthly rainfall maps were inverse distance weighting (IDW), ordinary kriging (OK), kriging with external drift (KED), and ordinary cokriging (COK). Their performance was assessed by the cross-validation and visual examination of the

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Janett, Gioele, Oskar Steiner, Ernest Alsina Ballester, Luca Belluzzi, and Siddhartha Mishra. "A novel fourth-order WENO interpolation technique." Astronomy & Astrophysics 624 (April 2019): A104. http://dx.doi.org/10.1051/0004-6361/201834761.

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Context. Several numerical problems require the interpolation of discrete data that present at the same time (i) complex smooth structures and (ii) various types of discontinuities. The radiative transfer in solar and stellar atmospheres is a typical example of such a problem. This calls for high-order well-behaved techniques that are able to interpolate both smooth and discontinuous data. Aims. This article expands on different nonlinear interpolation techniques capable of guaranteeing high-order accuracy and handling discontinuities in an accurate and non-oscillatory fashion. The final aim i

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Beckers, J. M., A. Barth, I. Tomazic, and A. Alvera-Azcárate. "A method to generate fully multi-scale optimal interpolation by combining efficient single process analyses, illustrated by a DINEOF analysis spiced with a local optimal interpolation." Ocean Science 10, no. 5 (2014): 845–62. http://dx.doi.org/10.5194/os-10-845-2014.

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Abstract. We present a method in which the optimal interpolation of multi-scale processes can be expanded into a succession of simpler interpolations. First, we prove how the optimal analysis of a superposition of two processes can be obtained by different mathematical formulations involving iterations and analysis focusing on a single process. From the different mathematical equivalent formulations, we then select the most efficient ones by analyzing the behavior of the different possibilities in a simple and well-controlled test case. The clear guidelines deduced from this experiment are the

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Sharples, Jason J., Michael F. Hutchinson, and Damian R. Jellett. "On the Horizontal Scale of Elevation Dependence of Australian Monthly Precipitation." Journal of Applied Meteorology 44, no. 12 (2005): 1850–65. http://dx.doi.org/10.1175/jam2289.1.

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Abstract Determination of the scale of the interaction between precipitation and topography is important for the accurate interpolation of rainfall in mountainous areas and also provides insight into the physical processes involved. In this paper, trivariate thin-plate smoothing splines are used to investigate the scale of interaction between monthly precipitation and topography by interpolating monthly rainfall over three subregions of the Australian continent, incorporating different climatic conditions and rainfall types. The interpolations are based upon elevations derived from digital ele

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Hakim, Denny. "Calderon's Complex Interpolation of Morrey Spaces." Journal of the Indonesian Mathematical Society 26, no. 1 (2020): 137–64. http://dx.doi.org/10.22342/jims.26.1.818.137-164.

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In this note we will discuss some results related to complex interpolation of Morreyspaces. We first recall the Riesz-Thorin interpolation theorem in Section 1.After that, we discuss a partial generalization of this theorem in Morrey spaces proved in \cite{St}.We also discuss non-interpolation property of Morrey spaces given in \cite{BRV99, RV}.In Section 3, we recall the definition of Calder\'on's complex interpolation method andthe description of complex interpolation of Lebesgue spaces.In Section 4, we discuss the description of complex interpolation of Morrey spaces given in\cite{CPP98, HS

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Celis, Oliver Salazar. "Numerical continued fraction interpolation." Ukrains’kyi Matematychnyi Zhurnal 74, no. 4 (2024): 568–80. http://dx.doi.org/10.3842/umzh.v74i4.7349.

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UDC 517.524 We show that highly accurate approximations can often be obtained by constructing Thiele interpolating continued fractions by a Greedy selection of the interpolation points together with an early termination condition. The obtained results are comparable with the outcome of state-of-the-art rational interpolation techniques based on the barycentric form.

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Hayotov, A. R., F. A. Nuraliev, and G. Sh Abdullaeva. "The Coeffisients of the Spline Minimizing Semi Norm in K2(P3)." International Journal of Analysis and Applications 23 (January 2, 2025): 7. https://doi.org/10.28924/2291-8639-23-2025-7.

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Our goal is to construct an approximation of the unknown function f by Sobolev’s method, we construct an approximation form of unknown function by interpolation splines minimizing the semi norm in K2(P3) Hilbert space. Explicit formulas for coefficients of the interpolation splines are obtained. The resulting interpolation spline is exact for the hyperbolic functions and constant. In the last section, we obtain several absolute errors graph in interpolating functions with the sixth order algebraic-hyperbolic spline, and we compare absolute errors of cubic spline and algebraic-hyperbolic in int

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Ren, Xiao Zhong, Ya Hui Wang, and Jian Xin Su. "Research on NC Dressing of Involute Grinding Wheel." Key Engineering Materials 455 (December 2010): 132–36. http://dx.doi.org/10.4028/www.scientific.net/kem.455.132.

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Aiming at the dressing of involute grinding wheel, the mathematical model of involute interpolation is established. Taking the normal tolerance δ as accuracy index, the dense degree of interpolation points can be changed constantly with the change of developable angle increment △θ so that the numbers of interpolation points can meet the requirements not only for interpolating accuracy, but for interpolating efficiency. The wheel dressing software developed by using VC++ as programming tool can be applied for dressing the involute grinding wheel which can be used to grind involute gears with di

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Al-Jawfi, Rashad A. "3D Fractal Interpolation Functions." Nanoscience and Nanotechnology Letters 12, no. 1 (2020): 120–23. http://dx.doi.org/10.1166/nnl.2020.3081.

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For visualizing one, two- and/or three-dimensional data, reconstruction mechanism is generally considered. In the present study, I have examined the application of iterated function systems in interpolation. I have also presented new fractal interpolation derivations for three-dimensional scalar data. The interpolations can indicate uncertainty of the data, allow tenability from the data, represent the data statistically at different scales, and may also more accurately facilitate data analysis.

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Bedi, S., I. Ali, and N. Quan. "Advanced Interpolation Techniques for N.C. Machines." Journal of Engineering for Industry 115, no. 3 (1993): 329–36. http://dx.doi.org/10.1115/1.2901668.

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This paper describes two methods for curve and surface interpolation. The layout of the machine and the implementation of these methods on an N.C. machine are discussed. The requirement for additional computational power to implement these interpolation methods is addressed by a network of computers called transputers. The interface between the controller and the network is described. This network also provides the ability to do interference checking in real time using the subdivision technique. The advantage of this implementation is that it enhances the ability of the conventional controller

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Jin, Yong Qiao, Yu Han Wang, and Jian Guo Yang. "Real-Time B-Spline Interpolator with Look-Ahead Scheme for High-Speed CNC Machine Tools." Key Engineering Materials 455 (December 2010): 599–605. http://dx.doi.org/10.4028/www.scientific.net/kem.455.599.

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NC tool paths of digital CAD models are currently generated as a set of discrete data points. The CNC interpolator must convert these points into continuous machine tool axis motions. In order to achieve high-speed and high-accuracy machining, the development of a real-time interpolation algorithm is really indispensable, which can deal with a large number of short blocks and still maintain smooth interpolation with an optimal speed. In this paper, a real-time local cubic B-spline interpolator with look-ahead scheme is proposed for consecutive micro-line blocks interpolation. First, the consec

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Sahrom, Nor Ashikin, and Mohammad Izat Emir Zulkifly. "Interval-Valued Fuzzy Bézier Curve Interpolation Model and its Visualization." Journal of Advanced Research in Computing and Applications 36, no. 1 (2024): 61–69. https://doi.org/10.37934/arca.36.1.6169.

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Curve interpolation is a crucial aspect in several applications, however, traditional approaches often face difficulties in handling data uncertainty and imprecision. This study presents a new interval-valued fuzzy Bézier curve interpolation model designed to address these difficulties effectively. In this paper, interval-valued fuzzy Bézier curve interpolation is introduced. The interval-valued fuzzy control points is defined as the data points to utilizes Bézier blending algorithms to provide smooth and accurate interpolations. In addition, a visualization method is presented to aid in under

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