Log in

Relevant bibliographies by topics / Operator split / Journal articles

To see the other types of publications on this topic, follow the link: Operator split.

Journal articles on the topic 'Operator split'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Operator split.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Zhao, Jing, and Hang Zhang. "Solving Split Common Fixed-Point Problem of Firmly Quasi-Nonexpansive Mappings without Prior Knowledge of Operators Norms." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/389689.

Full text

Abstract:

Very recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms for the split common fixed-point problem concerned two bounded linear operators. However, to employ Moudafi’s algorithms, one needs to know a prior norm (or at least an estimate of the norm) of the bounded linear operators. To estimate the norm of an operator is very difficult, if it is not an impossible task. It is the purpose of this paper to introduce a viscosity iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information about the operator norms. We prove the strong convergence of the proposed algorithms for split common fixed-point problem governed by the firmly quasi-nonexpansive operators. As a consequence, we obtain strong convergence theorems for split feasibility problem and split common null point problems of maximal monotone operators. Our results improve and extend the corresponding results announced by many others.

APA, Harvard, Vancouver, ISO, and other styles

2

Bandrauk, André D., and Hai Shen. "Higher order exponential split operator method for solving time-dependent Schrödinger equations." Canadian Journal of Chemistry 70, no. 2 (February 1, 1992): 555–59. http://dx.doi.org/10.1139/v92-078.

Full text

Abstract:

A new method of splitting exponential operators is proposed for the exponential form of the operator solution to the time-dependent Schrödinger equation. The method is shown to hold for any desired accuracy in the time increment. A comparison of different algorithms is made as a function of accuracy and computation time. Keywords: splitting operator, Fast Fourier Transform (FFT), Schrödinger equations.

APA, Harvard, Vancouver, ISO, and other styles

3

Gupta, Nishu, Mihai Postolache, Ashish Nandal, and Renu Chugh. "A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm." Mathematics 9, no. 4 (February 13, 2021): 372. http://dx.doi.org/10.3390/math9040372.

Full text

Abstract:

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

APA, Harvard, Vancouver, ISO, and other styles

4

Jailoka, Pachara, and Suthep Suantai. "Viscosity approximation methods for split common fixed point problems without prior knowledge of the operator norm." Filomat 34, no. 3 (2020): 761–77. http://dx.doi.org/10.2298/fil2003761j.

Full text

Abstract:

In this work, we study the split common fixed point problem which was first introduced by Censor and Segal [14]. We introduce an algorithm based on the viscosity approximation method without prior knowledge of the operator norm by selecting the stepsizes in the same adaptive way as L?opez et al. [22] for solving the problem for two attracting quasi-nonexpansive operators in real Hilbert spaces. A strong convergence result of the proposed algorithm is established under some suitable conditions. We also modify our algorithm to extend to the class of demicontractive operators and the class of hemicontractive operators, and obtain strong convergence results. Moreover, we apply our main result to other split problems, that is, the split feasibility problem and the split variational inequality problem. Finally, a numerical result is also given to illustrate the convergence behavior of our algorithm.

APA, Harvard, Vancouver, ISO, and other styles

5

Li, Meixia, Xueling Zhou, and Haitao Che. "Mixed Simultaneous Iterative Algorithms for the Extended Multiple-Set Split Equality Common Fixed-Point Problem with Lipschitz Quasi-Pseudocontractive Operators." Mathematical Problems in Engineering 2019 (March 7, 2019): 1–10. http://dx.doi.org/10.1155/2019/3606294.

Full text

Abstract:

In this paper, we study a kind of extended multiple-set split equality common fixed-point problem with Lipschitz quasi-pseudocontractive operators, which is an extension of multiple-set split equality common fixed-point problem with quasi-nonexpansive operator. We propose two mixed simultaneous iterative algorithms, in which the selecting of the stepsize does not need any priori information about the operator norms. Furthermore, we prove that the sequences generated by the mixed simultaneous iterative algorithms converge weakly to the solution of this problem. Some numerical results are shown to illustrate the feasibility and efficiency of the proposed algorithms.

APA, Harvard, Vancouver, ISO, and other styles

6

Yevick, D., W. Bardyszewski, B. Hermansson, and M. Glasner. "Split-operator electric field reflection techniques." IEEE Photonics Technology Letters 3, no. 6 (June 1991): 527–29. http://dx.doi.org/10.1109/68.91023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Kitkuan, Duangkamon, Poom Kumam, Vasile Berinde, and Anantachai Padcharoen. "Adaptive algorithm for solving the SCFPP of demicontractive operators without a priori knowledge of operator norms." Analele Universitatii "Ovidius" Constanta - Seria Matematica 27, no. 3 (December 1, 2019): 153–75. http://dx.doi.org/10.2478/auom-2019-0039.

Full text

Abstract:

AbstractIn this paper, we study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without a priori knowledge of operator norms. A strong convergence theorem is obtained under some additional conditions and numerical examples are included to illustrate the applications in signal compressed sensing and image restoration.

APA, Harvard, Vancouver, ISO, and other styles

8

DATTA, ALAKABHA, and XINMIN ZHANG. "VACUUM STABILITY IN SPLIT SUSY AND LITTLE HIGGS MODELS." International Journal of Modern Physics A 21, no. 11 (April 30, 2006): 2431–45. http://dx.doi.org/10.1142/s0217751x06029521.

Full text

Abstract:

We study the stability of the effective Higgs potential in the split supersymmetry and Little Higgs models. In particular, we study the effects of higher dimensional operators in the effective potential on the Higgs mass predictions. We find that the size and sign of the higher dimensional operators can significantly change the Higgs mass required to maintain vacuum stability in Split SUSY models. In the Little Higgs models the effects of higher dimensional operators can be large because of a relatively lower cutoff scale. Working with a specific model we find that a contribution from the higher dimensional operator with coefficient of O(1) can destabilize the vacuum.

APA, Harvard, Vancouver, ISO, and other styles

9

Čiegis, Raimondas, Aleksas Mirinavičius, and Mindaugas Radziunas. "Comparison of Split Step Solvers for Multidimensional Schrödinger Problems." Computational Methods in Applied Mathematics 13, no. 2 (April 1, 2013): 237–50. http://dx.doi.org/10.1515/cmam-2013-0004.

Full text

Abstract:

Abstract. This paper presents the analysis of the split step solvers for multidimensional Schrödinger problems. The second-order symmetrical splitting techniques are applied. The standard operator splitting is used to split the linear diffraction and reaction/potential processes. The dimension splitting exploits the commuting property of one-dimensional discrete diffraction operators. Alternating Direction Implicit (ADI) and Locally One-Dimensional (LOD) algorithms are constructed and stability is investigated for two- and three-dimensional problems. Compact high-order approximations are applied to discretize diffraction operators. Results of numerical experiments are presented and convergence of finite difference schemes is investigated.

APA, Harvard, Vancouver, ISO, and other styles

10

Ristow, Dietrich, and Thomas Rühl. "Fourier finite‐difference migration." GEOPHYSICS 59, no. 12 (December 1994): 1882–93. http://dx.doi.org/10.1190/1.1443575.

Full text

Abstract:

Many existing migration schemes cannot simultaneously handle the two most important problems of migration: imaging of steep dips and imaging in media with arbitrary velocity variations in all directions. For example, phase‐shift (ω, k) migration is accurate for nearly all dips but it is limited to very simple velocity functions. On the other hand, finite‐difference schemes based on one‐way wave equations consider arbitrary velocity functions but they attenuate steeply dipping events. We propose a new hybrid migration method, named “Fourier finite‐difference migration,” wherein the downward‐continuation operator is split into two downward‐continuation operators: one operator is a phase‐shift operator for a chosen constant background velocity, and the other operator is an optimized finite‐difference operator for the varying component of the velocity function. If there is no variation of velocity, then only a phase‐shift operator will be applied automatically. On the other hand, if there is a strong variation of velocity, then the phase‐shift component is suppressed and the optimized finite‐difference operator will be fully applied. The cascaded application of phase‐shift and finite‐difference operators shows a better maximum dip‐angle behavior than the split‐step Fourier migration operator. Depending on the macro velocity model, the Fourier finite‐difference migration even shows an improved performance compared to conventional finite‐difference migration with one downward‐continuation step. Finite‐difference migration with two downward‐continuation steps is required to reach the same migration performance, but this is achieved with about 20 percent higher computation costs. The new cascaded operator of the Fourier finite‐difference migration can be applied to arbitrary velocity functions and allows an accurate migration of steeply dipping reflectors in a complex macro velocity model. The dip limitation of the cascaded operator depends on the variation of the velocity field and, hence, is velocity‐adaptive.

APA, Harvard, Vancouver, ISO, and other styles

11

Li, Meixia, Xueling Zhou, and Wenchao Wang. "Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem." Journal of Function Spaces 2020 (June 3, 2020): 1–15. http://dx.doi.org/10.1155/2020/6034754.

Full text

Abstract:

In this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projection and obtain the weak and the strong convergence of the algorithms, respectively. Furthermore, based on the operators being quasinonexpansive, we offer an iterative algorithm to solve the extended split equality fixed point problem. We introduce a way of selecting the stepsize which does not need any prior information about operator norms in the three algorithms. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.

APA, Harvard, Vancouver, ISO, and other styles

12

Kaplan, Sam T., Partha S. Routh, and Mauricio D. Sacchi. "Derivation of forward and adjoint operators for least-squares shot-profile split-step migration." GEOPHYSICS 75, no. 6 (November 2010): S225—S235. http://dx.doi.org/10.1190/1.3506146.

Full text

Abstract:

The forward and adjoint operators for shot-profile least-squares migration are derived. The forward operator is demigration, and the adjoint operator is migration. The demigration operator is derived from the Born approximation. The process begins with a Green’s function that allows for a laterally varying migration velocity model using the split-step approximation. Next, the earth is divided into horizontal layers, and within each layer the migration velocity model is made to be constant with respect to depth. For a given layer, (1) the source-side wavefield is propagated down to its top using the background wavefield. This gives a background wavefield incident at the layer’s upper boundary. (2) The layer’s contribution to the scattered wavefield is computed using the Born approximation to the scattered wavefield and the background wavefield. (3) Next, its scattered wavefield is propagated back up to the measurement surface using, again, the background wavefield. The measured wavefield is approximated by the sum of scattered wavefields from each layer. In the derivation of the measured wavefield, the shot-profile migration geometry is used. For each shot, the resulting wavefield modeling operator takes the form of a Fredholm integral equation of the first kind, and this is used to write down its adjoint, the shot-profile migration operator. This forward/adjoint pair is used for shot-profile least-squares migration. Shot-profile least-squares migration is illustrated with two synthetic examples. The first uses data collected over a four-layer acoustic model, and the second uses data from the Sigsbee 2a model.

APA, Harvard, Vancouver, ISO, and other styles

13

Oyewole, Olawale Kazeem, and Oluwatosin Temitope Mewomo. "A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces." Axioms 10, no. 1 (February 5, 2021): 16. http://dx.doi.org/10.3390/axioms10010016.

Full text

Abstract:

In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature.

APA, Harvard, Vancouver, ISO, and other styles

14

Ogbuisi, Ferdinard U., and Oluwatosin T. Mewomo. "Convergence analysis of an inertial accelerated iterative algorithm for solving split variational inequality problem." Advances in Pure and Applied Mathematics 10, no. 4 (October 1, 2019): 339–53. http://dx.doi.org/10.1515/apam-2017-0132.

Full text

Abstract:

AbstractIn this paper, we introduce an iterative scheme involving an inertial term and a step size independent of the operator norm for approximating a solution to a split variational inequality problem in a real Hilbert space. Furthermore, we prove a convergence theorem for the sequence generated by the proposed operator norm independent inertial accelerated iterative scheme. We applied our result to solve split convex minimization problems, split zero problem and further give a numerical example to demonstrate the efficiency of the proposed algorithm.

APA, Harvard, Vancouver, ISO, and other styles

15

Jirakitpuwapat, Wachirapong, Poom Kumam, Yeol Cho, and Kanokwan Sitthithakerngkiet. "A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing." Mathematics 7, no. 3 (February 28, 2019): 226. http://dx.doi.org/10.3390/math7030226.

Full text

Abstract:

In 2014, Cui and Wang constructed an algorithm for demicontractive operators and proved some weak convergence theorems of their proposed algorithm to show the existence of solutions for the split common fixed point problem without using the operator norm. By Cui and Wang’s motivation, in 2015, Boikanyo constructed also a new algorithm for demicontractive operators and obtained some strong convergence theorems for this problem without using the operator norm. In this paper, we consider a viscosity iterative algorithm in Boikanyo’s algorithm to approximate to a solution of this problem and prove some strong convergence theorems of our proposed algorithm to a solution of this problem. Finally, we apply our main results to some applications, signal processing and others and compare our algorithm with five algorithms such as Cui and Wang’s algorithm, Boikanyo’s algorithm, forward-backward splitting algorithm and the fast iterative shrinkage-thresholding algorithm (FISTA).

APA, Harvard, Vancouver, ISO, and other styles

16

LIVNY, YOTAM, NETA SOKOLOVSKY, and JIHAD EL-SANA. "DUAL ADAPTIVE PATHS FOR MULTIRESOLUTION HIERARCHIES." International Journal of Image and Graphics 07, no. 02 (April 2007): 273–90. http://dx.doi.org/10.1142/s0219467807002726.

Full text

Abstract:

The recent increase in the generated polygonal dataset sizes has outpaced the performance of graphics hardware. Several solutions such as multiresolution hierarchies and level-of-detail rendering have been developed to bridge the increasing gap. However, the discrete levels of detail generate annoying popping effects, the preliminaries multiresolution schemes cannot perform drastic changes on the selected level of detail within the span of small number of frames, and the current cluster-based hierarchies suffer from the high-detailed representation of the boundaries between clusters. In this paper, we are presenting a novel approach for multiresolution hierarchy that supports dual paths for run-time adaptive simplification — fine and coarse. The proposed multiresolution hierarchy is based on the fan-merge operator and its reverse operator fan-split. The coarse simplification path is achieved by directly applying fan-merge/split, while the fine simplification route is performed by executing edge-collapse/vertex-split one at a time. The sequence of the edge-collapses/vertex-splits is encoded implicitly by the order of the children participating in the fan-merge/split operator. We shall refer to this multiresolution hierarchy as fan-hierarchy. Fan-hierarchy provides a compact data structure for multiresolution hierarchy, since it stores 7/6 pointers, on the average, instead of 3 pointers for each node. In addition, the resulting depth of the fan-hierarchy is usually smaller than the depth of hierarchies generated by edge-collapse based multiresolution schemes. It is also important to note that fan-hierarchy inherently utilizes fan representation for further acceleration of the rendering process.

APA, Harvard, Vancouver, ISO, and other styles

17

Gracheva, I. A., and A. V. Kopylov. "TONE COMPRESSION ALGORITHM FOR HIGH DYNAMIC RANGE MEDICAL IMAGES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W12 (May 9, 2019): 87–95. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w12-87-2019.

Full text

Abstract:

<p><strong>Abstract.</strong> We propose here an HDR compression method for medical images based on a windowing operator, an adaptive tone mapping operator, and the probabilistic normal-gamma model. First, we use the windowing operator based on a structural fidelity measure for optimal visualization of the input HDR medical image. Then, we transform the windowed image to the logarithm domain and split it into base and detail layers with the help of the probabilistic normal-gamma model. Base and detail layers are used to make the tone map with help the adaptive tone mapping operator. Finally, the tone mapping result is the LDR image. The proposed method has comparable quality and low computation time compared to other tone mapping operators.</p>

APA, Harvard, Vancouver, ISO, and other styles

18

Hong, Chung-Chien, and Young-Ye Huang. "A Strong Convergence Algorithm for the Two-Operator Split Common Fixed Point Problem in Hilbert Spaces." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/350479.

Full text

Abstract:

The two-operator split common fixed point problem (two-operator SCFP) with firmly nonexpansive mappings is investigated in this paper. This problem covers the problems of split feasibility, convex feasibility, and equilibrium and can especially be used to model significant image recovery problems such as the intensity-modulated radiation therapy, computed tomography, and the sensor network. An iterative scheme is presented to approximate the minimum norm solution of the two-operator SCFP problem. The performance of the presented algorithm is compared with that of the last algorithm for the two-operator SCFP and the advantage of the presented algorithm is shown through the numerical result.

APA, Harvard, Vancouver, ISO, and other styles

19

Yevick, D., J. Xu, and W. Bardyszewski. "Split-operator calculations of reflected electric field profiles." IEEE Photonics Technology Letters 4, no. 12 (December 1992): 1383–86. http://dx.doi.org/10.1109/68.180584.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Li, Chi Wai. "A split operator scheme for ocean wave simulation." International Journal for Numerical Methods in Fluids 15, no. 5 (September 15, 1992): 579–93. http://dx.doi.org/10.1002/fld.1650150506.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Boikanyo, Oganeditse A., and Habtu Zegeye. "Split equality variational inequality problems for pseudomonotone mappings in Banach spaces." Studia Universitatis Babes-Bolyai Matematica 66, no. 1 (March 20, 2021): 139–58. http://dx.doi.org/10.24193/subbmath.2021.1.13.

Full text

Abstract:

"A new algorithm for approximating solutions of the split equality variational inequality problems (SEVIP) for pseudomonotone mappings in the setting of Banach spaces is introduced. Strong convergence of the sequence generated by the proposed algorithm to a solution of the SEVIP is then derived without assuming the Lipschitz continuity of the underlying mappings and without prior knowledge of operator norms of the bounded linear operators involved. In addition, we provide several applications of our method and provide a numerical example to illustrate the convergence of the proposed algorithm. Our results improve, consolidate and complement several results reported in the literature."

APA, Harvard, Vancouver, ISO, and other styles

22

Zhang, Jianfeng, and Linong Liu. "Optimum split-step Fourier 3D depth migration: Developments and practical aspects." GEOPHYSICS 72, no. 3 (May 2007): S167—S175. http://dx.doi.org/10.1190/1.2715658.

Full text

Abstract:

We present an efficient scheme for depth extrapolation of wide-angle 3D wavefields in laterally heterogeneous media. The scheme improves the so-called optimum split-step Fourier method by introducing a frequency-independent cascaded operator with spatially varying coefficients. The developments improve the approximation of the optimum split-step Fourier cascaded operator to the exact phase-shift operator of a varying velocity in the presence of strong lateral velocity variations, and they naturally lead to frequency-dependent varying-step depth extrapolations that reduce computational cost significantly. The resulting scheme can be implemented alternatively in spatial and wavenumber domains using fast Fourier transforms (FFTs). The accuracy of the first-order approximate algorithm is similar to that of the second-order optimum split-step Fourier method in modeling wide-angle propagation through strong, laterally varying media. Similar to the optimum split-step Fourier method, the scheme is superior to methods such as the generalized screen and Fourier finite difference. We demonstrate the scheme’s accuracy by comparing it with 3D two-way finite-difference modeling. Comparisons with the 3D prestack Kirchhoff depth migration of a real 3D data set demonstrate the practical application of the proposed method.

APA, Harvard, Vancouver, ISO, and other styles

23

Dattoli, G., L. Giannessi, P. L. Ottaviani, and A. Torre. "Split-operator technique and solution of Liouville propagation equations." Physical Review E 51, no. 1 (January 1, 1995): 821–24. http://dx.doi.org/10.1103/physreve.51.821.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Dumitru, Raluca, Costel Peligrad, and Bogdan Visinescu. "Reflexivity of operator algebras of finite split strict multiplicity." Operators and Matrices, no. 2 (2011): 221–26. http://dx.doi.org/10.7153/oam-05-15.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Braun, Michael, Christoph Meier, and Volker Engel. "Nanosecond wave-packet propagation with the Split-Operator Technique." Computer Physics Communications 93, no. 2-3 (February 1996): 152–58. http://dx.doi.org/10.1016/0010-4655(95)00132-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Connors, Jeffrey M., Jeffrey W. Banks, Jeffrey A. Hittinger, and Carol S. Woodward. "Quantification of errors for operator-split advection–diffusion calculations." Computer Methods in Applied Mechanics and Engineering 272 (April 2014): 181–97. http://dx.doi.org/10.1016/j.cma.2014.01.005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Xu, Hong-Kun, and Andrzej Cegielski. "The Landweber Operator Approach to the Split Equality Problem." SIAM Journal on Optimization 31, no. 1 (January 2021): 626–52. http://dx.doi.org/10.1137/20m1337910.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

YAO, YONGHONG, JEN-CHIH YAO, YEONG-CHENG LIOU, and MIHAI POSTOLACHE. "Iterative algorithms for split common fixed points of demicontractive operators without priori knowledge of operator norms." Carpathian Journal of Mathematics 34, no. 3 (2018): 459–66. http://dx.doi.org/10.37193/cjm.2018.03.23.

Full text

Abstract:

The split common fixed points problem for demicontractive operators has been studied in Hilbert spaces. An iterative algorithm is considered and the weak convergence result is given under some mild assumptions.

APA, Harvard, Vancouver, ISO, and other styles

29

Wu, Xiufeng, Junjie Huang, and Alatancang Chen. "The point spectrum and residual spectrum of upper triangular operator matrices." Filomat 33, no. 6 (2019): 1759–71. http://dx.doi.org/10.2298/fil1906759w.

Full text

Abstract:

The point and residual spectra of an operator are, respectively, split into 1,2-point spectrum and 1,2-residual spectrum, based on the denseness and closedness of its range. Let H,K be infinite dimensional complex separable Hilbert spaces and write MX = (AX0B) ? B(H?K). For given operators A ? B(H) and B ? B(K), the sets ? X?B(K,H) ?+,i(MX)(+ = p,r;i = 1,2), are characterized. Moreover, we obtain some necessary and sufficient condition such that ?*,i(MX) = ?*,i(A) ?*,i(B) (* = p,r;i = 1,2) for every X ? B(K,H).

APA, Harvard, Vancouver, ISO, and other styles

30

Fegan, H. D., and B. Steer. "First Order Operators on Manifolds With a Group Action." Canadian Journal of Mathematics 48, no. 4 (August 1, 1996): 758–76. http://dx.doi.org/10.4153/cjm-1996-039-6.

Full text

Abstract:

AbstractWe investigate questions of spectral symmetry for certain first order differential operators acting on sections of bundles over manifolds which have a group action. We show that if the manifold is in fact a group we have simple spectral symmetry for all homogeneous operators. Furthermore if the manifold is not necessarily a group but has a compact Lie group of rank 2 or greater acting on it by isometries with discrete isotropy groups, and let D be a split invariant elliptic first order differential operator, then D has equivariant spectral symmetry.

APA, Harvard, Vancouver, ISO, and other styles

31

López, Genaro, Victoria Martín-Márquez, Fenghui Wang, and Hong-Kun Xu. "Forward-Backward Splitting Methods for Accretive Operators in Banach Spaces." Abstract and Applied Analysis 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/109236.

Full text

Abstract:

Splitting methods have recently received much attention due to the fact that many nonlinear problems arising in applied areas such as image recovery, signal processing, and machine learning are mathematically modeled as a nonlinear operator equation and this operator is decomposed as the sum of two (possibly simpler) nonlinear operators. Most of the investigation on splitting methods is however carried out in the framework of Hilbert spaces. In this paper, we consider these methods in the setting of Banach spaces. We shall introduce two iterative forward-backward splitting methods with relaxations and errors to find zeros of the sum of two accretive operators in the Banach spaces. We shall prove the weak and strong convergence of these methods under mild conditions. We also discuss applications of these methods to variational inequalities, the split feasibility problem, and a constrained convex minimization problem.

APA, Harvard, Vancouver, ISO, and other styles

32

Liu, Linong, and Jianfeng Zhang. "3D wavefield extrapolation with optimum split-step Fourier method." GEOPHYSICS 71, no. 3 (May 2006): T95—T108. http://dx.doi.org/10.1190/1.2197493.

Full text

Abstract:

A one-way propagator is proposed for more accurately modeling wide-angle wavefields in the presence of severe lateral variations of the velocity. The method adds a higher-order correction to improve the split-step Fourier method by directly designing a cascaded operator that matches the exact phase-shift operator of a varying velocity. Using an optimization scheme, the coefficients in the cascaded operator are determined according to the local velocity distribution and the prescribed angular range of wavefield propagation. The proposed algorithm is implemented alternately in spatial and wavenumber domains using fast Fourier transforms, as in the split-step Fourier and generalized-screen methods. This algorithm can achieve higher accuracy than the generalized-screen method for wide-angle wavefields, although the same numerical scheme is used with comparable computational cost. No extra error arises for the proposed algorithm when used for 3D wave propagation, in contrast to methods that introduce an implicit finite–difference higher-order correction to the split-step Fourier method, such as the Fourier finite difference (FFD) and wide-angle screen methods. A detailed comparison of the proposed one-way propagator with the split-step Fourier, generalized-screen, and FFD methods is presented. The 2D Marmousi and 3D SEG/EAEG overthrust data sets are used to test the prestack depth-migration schemes developed based on the proposed one-way propagators.

APA, Harvard, Vancouver, ISO, and other styles

33

Zhao, Jing, and Songnian He. "Solving the general split common fixed-point problem of quasi-nonexpansive mappings without prior knowledge of operator norms." Filomat 31, no. 3 (2017): 559–73. http://dx.doi.org/10.2298/fil1703559z.

Full text

Abstract:

Let H1, H2, H3 be real Hilbert spaces, let A : H1 ? H3, B : H2 ? H3 be two bounded linear operators. The general multiple-set split common fixed-point problem under consideration in this paper is to find x ??p,i=1F(Ui), y ??r,j=1 F(Tj) such that Ax = Bym, (1) where p, r ? 1 are integers, Ui : H1 ? H1 (1 ? i ? p) and Tj : H2 ? H2 (1 ? j ? r) are quasi-nonexpansive mappings with nonempty common fixed-point sets ?p,i=1 F(Ui) = ?p,i=1 {x ? H1 : Uix = x} and ?r,j=1F(Tj) = ?r,j=1 {x ? H2 : Tjx = x}. Note that, the above problem (1) allows asymmetric and partial relations between the variables x and y. If H2 = H3 and B = I, then the general multiple-set split common fixed-point problem (1) reduces to the multiple-set split common fixed-point problem proposed by Censor and Segal [J. Convex Anal. 16(2009), 587-600]. In this paper, we introduce simultaneous parallel and cyclic algorithms for the general split common fixed-point problems (1). We introduce a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. We prove the weak convergence of the proposed algorithms and apply the proposed algorithms to the multiple-set split feasibility problems. Our results improve and extend the corresponding results announced by many others.

APA, Harvard, Vancouver, ISO, and other styles

34

Ahmed, A. H. "Computable error bounds with improved applicability conditions for collocation methods." International Journal of Mathematics and Mathematical Sciences 21, no. 2 (1998): 375–79. http://dx.doi.org/10.1155/s0161171298000519.

Full text

Abstract:

This paper is concerned with error bounds for numerical solution of linear ordinary differential equation using collocation method. It is shown that if the differential operator is split in different operator forms then the applicability conditions for the computable error bounds which are based on the collocation matrices could be improved

APA, Harvard, Vancouver, ISO, and other styles

35

Wang, Yaqin, Tae-Hwa Kim, and Xiaoli Fang. "Weak and Strong Convergence Theorems for the Multiple-Set Split Equality Common Fixed-Point Problems of Demicontractive Mappings." Journal of Function Spaces 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/5306802.

Full text

Abstract:

We consider mixed parallel and cyclic iterative algorithms in this paper to solve the multiple-set split equality common fixed-point problem which is a generalization of the split equality problem and the split feasibility problem for the demicontractive mappings without prior knowledge of operator norms in real Hilbert spaces. Some weak and strong convergence results are established. The results obtained in this paper generalize and improve the recent ones announced by many others.

APA, Harvard, Vancouver, ISO, and other styles

36

Tolstunov, Len. "Classification of the Alveolar Ridge Width: Implant-Driven Treatment Considerations for the Horizontally Deficient Alveolar Ridges." Journal of Oral Implantology 40, S1 (July 1, 2014): 365–70. http://dx.doi.org/10.1563/aaid-joi-d-14-00023.

Full text

Abstract:

Among many techniques advocated for the horizontally deficient alveolar ridges, ridge-split has many advantages. Here, treatment management strategies of the horizontally collapsed ridges, especially the ridge-split approach, are discussed and a clinically relevant implant-driven classification of the alveolar ridge width is proposed, with the goal to assist an operator in choosing the proper bone augmentation technique. Comparison and advantages of two commonly used techniques, ridge-split and block bone graft, are presented.

APA, Harvard, Vancouver, ISO, and other styles

37

Bignell, Georgina Juanita, and Peter R. Johnston. "Split operator finite element method for modelling pulmonary gas exchange." ANZIAM Journal 49 (August 9, 2007): 364. http://dx.doi.org/10.21914/anziamj.v48i0.125.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Li, C. W., and F. Zhang. "Three‐dimensional simulation of thermals using a split‐operator scheme." International Journal of Numerical Methods for Heat & Fluid Flow 6, no. 2 (February 1996): 25–35. http://dx.doi.org/10.1108/09615539610113073.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Eno, Larry. "On the use of the second order split-operator method." Journal of Chemical Physics 113, no. 1 (July 2000): 453–54. http://dx.doi.org/10.1063/1.481810.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Yan, Ai-Ling, Gao-Yang Wang, and Naihua Xiu. "Robust solutions of split feasibility problem with uncertain linear operator." Journal of Industrial & Management Optimization 3, no. 4 (2007): 749–61. http://dx.doi.org/10.3934/jimo.2007.3.749.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Ullrich, Paul, and Christiane Jablonowski. "Operator-Split Runge–Kutta–Rosenbrock Methods for Nonhydrostatic Atmospheric Models." Monthly Weather Review 140, no. 4 (April 2012): 1257–84. http://dx.doi.org/10.1175/mwr-d-10-05073.1.

Full text

Abstract:

This paper presents a new approach for discretizing the nonhydrostatic Euler equations in Cartesian geometry using an operator-split time-stepping strategy and unstaggered upwind finite-volume model formulation. Following the method of lines, a spatial discretization of the governing equations leads to a set of coupled nonlinear ordinary differential equations. In general, explicit time-stepping methods cannot be applied directly to these equations because the large aspect ratio between the horizontal and vertical grid spacing leads to a stringent restriction on the time step to maintain numerical stability. Instead, an A-stable linearly implicit Rosenbrock method for evolving the vertical components of the equations coupled to a traditional explicit Runge–Kutta formula in the horizontal is proposed. Up to third-order temporal accuracy is achieved by carefully interleaving the explicit and linearly implicit steps. The time step for the resulting Runge–Kutta–Rosenbrock–type semi-implicit method is then restricted only by the grid spacing and wave speed in the horizontal. The high-order finite-volume model is tested against a series of atmospheric flow problems to verify accuracy and consistency. The results of these tests reveal that this method is accurate, stable, and applicable to a wide range of atmospheric flows and scales.

APA, Harvard, Vancouver, ISO, and other styles

42

Simpson, Matthew J., and Kerry A. Landman. "Characterizing and minimizing the operator split error for Fisher’s equation." Applied Mathematics Letters 19, no. 7 (July 2006): 604–12. http://dx.doi.org/10.1016/j.aml.2005.08.011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Cvitas, Marko T., and Stuart C. Althorpe. "Parallelizable split-operator propagator for treating Coriolis-coupled quantum dynamics." Computer Physics Communications 177, no. 4 (August 2007): 357–61. http://dx.doi.org/10.1016/j.cpc.2007.05.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Bauke, Heiko, and Christoph H. Keitel. "Accelerating the Fourier split operator method via graphics processing units." Computer Physics Communications 182, no. 12 (December 2011): 2454–63. http://dx.doi.org/10.1016/j.cpc.2011.07.003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Jolaoso, Lateef Olakunle, and Maggie Aphane. "A Generalized Viscosity Inertial Projection and Contraction Method for Pseudomonotone Variational Inequality and Fixed Point Problems." Mathematics 8, no. 11 (November 16, 2020): 2039. http://dx.doi.org/10.3390/math8112039.

Full text

Abstract:

We introduce a new projection and contraction method with inertial and self-adaptive techniques for solving variational inequalities and split common fixed point problems in real Hilbert spaces. The stepsize of the algorithm is selected via a self-adaptive method and does not require prior estimate of norm of the bounded linear operator. More so, the cost operator of the variational inequalities does not necessarily needs to satisfies Lipschitz condition. We prove a strong convergence result under some mild conditions and provide an application of our result to split common null point problems. Some numerical experiments are reported to illustrate the performance of the algorithm and compare with some existing methods.

APA, Harvard, Vancouver, ISO, and other styles

46

Skamarock, William C. "Positive-Definite and Monotonic Limiters for Unrestricted-Time-Step Transport Schemes." Monthly Weather Review 134, no. 8 (August 1, 2006): 2241–50. http://dx.doi.org/10.1175/mwr3170.1.

Full text

Abstract:

Abstract General positive-definite and monotonic limiters are described for use with unrestricted-Courant-number flux-form transport schemes. These limiters are tested using a time-split multidimensional transport scheme. The importance of minimizing the splitting errors associated with the time-split operator and of the consistency between the transport scheme and the discrete continuity equation is demonstrated.

APA, Harvard, Vancouver, ISO, and other styles

47

DADASHI, VAHID. "SHRINKING PROJECTION ALGORITHMS FOR THE SPLIT COMMON NULL POINT PROBLEM." Bulletin of the Australian Mathematical Society 96, no. 2 (March 29, 2017): 299–306. http://dx.doi.org/10.1017/s000497271700017x.

Full text

Abstract:

We consider the split common null point problem in Hilbert space. We introduce and study a shrinking projection method for finding a solution using the resolvent of a maximal monotone operator and prove a strong convergence theorem for the algorithm.

APA, Harvard, Vancouver, ISO, and other styles

48

Arntsen, Børge, Constantin Gerea, and Tage Røsten. "Imaging salt bodies using explicit migration operators offshore Norway." GEOPHYSICS 74, no. 2 (March 2009): S25—S32. http://dx.doi.org/10.1190/1.3063660.

Full text

Abstract:

We have tested the performance of 3D shot-profile depth migration using explicit migration operators on a real 3D marine data set. The data were acquired offshore Norway in an area with a complex subsurface containing large salt bodies. We compared shot-profile migration using explicit migration operators with conventional Kirchhoff migration, split-step Fourier migration, and common-azimuth by generalized screen propagator (GSP) migration in terms of quality and computational cost. Image quality produced by the explicit migration operator approach is slightly better than with split-step Fourier migration and clearly better than in common-azimuth by GSP and Kirchhoff migrations. The main differences are fewer artifacts and better-suppressed noise within the salt bodies. Kirchhoff migration shows considerable artifacts (migration smiles) within and close to the salt bodies, which are not present in images produced by the other three wave-equation methods. Expressions for computational cost were developed for all four migration algorithms in terms of frequency content and acquisition parameters. For comparable frequency content, migration cost using explicit operators is four times the cost of the split-step Fourier method, up to 260 times the cost of common-azimuth by GSP migration, and 25 times the cost of Kirchhoff migration. Our results show that in terms of image quality, shot-profile migration using explicit migration operators is well suited for imaging in areas with complex geology and significant velocity changes. However, computational cost of the method is high and makes it less attractive in terms of efficiency.

APA, Harvard, Vancouver, ISO, and other styles

49

Chaves, A., G. A. Farias, F. M. Peeters, and R. Ferreira. "The Split-Operator Technique for the Study of Spinorial Wavepacket Dynamics." Communications in Computational Physics 17, no. 3 (March 2015): 850–66. http://dx.doi.org/10.4208/cicp.110914.281014a.

Full text

Abstract:

AbstractThe split-operator technique for wave packet propagation in quantum systems is expanded here to the case of propagatingwave functions describing Schrödinger particles, namely, charge carriers in semiconductor nanostructures within the effective mass approximation, in the presence of Zeeman effect, as well as of Rashba and Dresselhaus spin-orbit interactions. We also demonstrate that simple modifications to the expanded technique allow us to calculate the time evolution of wave packets describing Dirac particles, which are relevant for the study of transport properties in graphene.

APA, Harvard, Vancouver, ISO, and other styles

50

Zhu, Wen-juan, Miao-miao Han, and Yi Zhao. "Electron Transfer Dynamics in Solution Using Imaginary-time Split Operator Approach." Chinese Journal of Chemical Physics 20, no. 3 (June 2007): 217–23. http://dx.doi.org/10.1088/1674-0068/20/03/217-223.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!