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1

Antipin, A. S. "Linearization method." Computational Mathematics and Modeling 8, no. 1 (January 1997): 1–15. http://dx.doi.org/10.1007/bf02404060.

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2

Pshenichnyj, B. N. "The linearization method." Optimization 18, no. 2 (January 1987): 179–96. http://dx.doi.org/10.1080/02331938708843231.

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3

Li, Jin, and Yongling Cheng. "Barycentric rational interpolation method for solving KPP equation." Electronic Research Archive 31, no. 5 (2023): 3014–29. http://dx.doi.org/10.3934/era.2023152.

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<abstract><p>In this paper, we seek to solve the Kolmogorov-Petrovskii-Piskunov (KPP) equation by the linear barycentric rational interpolation method (LBRIM). As there are non-linear parts in the KPP equation, three kinds of linearization schemes, direct linearization, partial linearization, Newton linearization, are presented to change the KPP equation into linear equations. With the help of barycentric rational interpolation basis function, matrix equations of three kinds of linearization schemes are obtained from the discrete KPP equation. Convergence rate of LBRIM for solving the KPP equation is also proved. At last, two examples are given to prove the theoretical analysis.</p></abstract>
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4

Calisal, S. M. "A Geometrically Consistent Linearization Method." Transactions of the Canadian Society for Mechanical Engineering 9, no. 2 (June 1985): 84–89. http://dx.doi.org/10.1139/tcsme-1985-0012.

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The study of irrotational incompressible flows about thin geometries can be carried out using the well known perturbation procedures. In two-dimensional flows exact solutions based on mappings can be used to compare the accuracy of first order solutions. For most airfoil sections a first order perturbation solution is not sufficiently accurate in representing the pressure and velocity distribution, especially about the leading edge. For three-dimensional flows exact solutions are rare and for more complex problems such as ship wave resistance formulations an exact solution does not exist for comparison of results. In this last case second-order solutions exist but are very difficult to calculate. Therefore, it would appear advantageous to improve first-order calculations. To this end a perturbation method that incorporates the geometric properties of the body is studied. This method is applied to a symmetric Joukowski airfoil and to an elipse. This method, here called the “geometrically-consistent linearization method” predicts the leading edge pressure variations correctly in the two cases studied and appears to be superior to the classical first order solutions. An iterative solution following this procedure further improves the calculation especially for thicker foils. The method discussed and the following iteration procedure seem to form an efficient numerical solution to airfoil flow problems.
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5

Halás, Miroslav, Mikuláš Huba, and Katarína Žáková. "The Exact Velocity Linearization Method." IFAC Proceedings Volumes 36, no. 18 (September 2003): 259–64. http://dx.doi.org/10.1016/s1474-6670(17)34678-5.

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6

Danilin, Yu M. "Linearization method using smooth penalties." Cybernetics and Systems Analysis 29, no. 4 (1994): 500–513. http://dx.doi.org/10.1007/bf01125864.

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7

Pho, Nguyen Van, and Le Ngoc Thach. "Linearization method in reliability problem." Vietnam Journal of Mechanics 15, no. 3 (September 30, 1993): 37–40. http://dx.doi.org/10.15625/0866-7136/10211.

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8

TANAKA, H. "Linearization Method and Linear Complexity." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E91-A, no. 1 (January 1, 2008): 22–29. http://dx.doi.org/10.1093/ietfec/e91-a.1.22.

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9

Leonov, G. A. "On the harmonic linearization method." Doklady Mathematics 79, no. 1 (February 2009): 144–46. http://dx.doi.org/10.1134/s1064562409010426.

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10

Li, Jin. "Linear barycentric rational interpolation method for solving Kuramoto-Sivashinsky equation." AIMS Mathematics 8, no. 7 (2023): 16494–510. http://dx.doi.org/10.3934/math.2023843.

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<abstract><p>The Kuramoto-Sivashinsky (KS) equation being solved by the linear barycentric rational interpolation method (LBRIM) is presented. Three kinds of linearization schemes, direct linearization, partial linearization and Newton linearization, are presented to get the linear equation of the Kuramoto-Sivashinsky equation. Matrix equations of the discrete Kuramoto-Sivashinsky equation are also given. The convergence rate of LBRIM for solving the KS equation is also proved. At last, two examples are given to prove the theoretical analysis.</p></abstract>
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11

Trom, J. D., and M. J. Vanderploeg. "Automated Linearization of Nonlinear Coupled Differential and Algebraic Equations." Journal of Mechanical Design 116, no. 2 (June 1, 1994): 429–36. http://dx.doi.org/10.1115/1.2919397.

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This paper presents a new approach for linearization of large multibody dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute linearizations for large-scale systems that were previously impossible.
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12

Li, Hong Jun, Qiang Ding, and Xun Huang. "A New Method of Stress Linearization for Design by Analysis in Pressure Vessel Design." Applied Mechanics and Materials 598 (July 2014): 194–97. http://dx.doi.org/10.4028/www.scientific.net/amm.598.194.

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Stress linearization is used to define constant and linear through-thickness FEA (Finite Element Analysis) stress distributions that are used in place of membrane and membrane plus bending stress distributions in pressure vessel Design by Analysis. In this paper, stress linearization procedures are reviewed with reference to the ASME Boiler & Pressure Vessel Code Section VIII Division 2 and EN13445. The basis of the linearization procedure is stated and a new method of stress linearization considering selected stress tensors for linearization is proposed.
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13

Zhou, Dao Chuan, Guo Rong Chen, and Li Ying Nie. "Application Effect Evaluation of Equivalent Linearization Method Used in Displacement-Based Design of Bridge Piers." Applied Mechanics and Materials 204-208 (October 2012): 2139–47. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.2139.

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Six equivalent linearization methods are summarized and calculation process of applying equivalent linearization method for displacement-based design of bridge engineering is studied. With the evaluation of volume stirrup ratio and safety performance of design structure, six different equivalent linearization methods are used in displacement-based design of bridge columns. The influence of equivalent linearization model and the damping adjust coefficient to seismic design results is studied. Study shows that there are big differences among the seismic design results based on different equivalent linearization methods. Equivalent damping ratio model and the damping adjust coefficient have great influence on seismic design results. Calculation errors of Kowalsky method and Iwan method and Ou method are very small. Calculation error of Kowalsky method is decreasing when displacement ductility factor increases. The calculated result based on the damping adjust coefficient provided by Eurocode8 specification is more close to the real one. Kowalsky method and the damping adjust coefficient of Eurocode8 specification is recommended to be used in displacement-based design of bridge engineering.
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14

Martinez, Dany Ivan, José de Jesús Rubio, Victor Garcia, Tomas Miguel Vargas, Marco Antonio Islas, Jaime Pacheco, Guadalupe Juliana Gutierrez, Jesus Alberto Meda-Campaña, Dante Mujica-Vargas, and Carlos Aguilar-Ibañez. "Transformed Structural Properties Method to Determine the Controllability and Observability of Robots." Applied Sciences 11, no. 7 (March 30, 2021): 3082. http://dx.doi.org/10.3390/app11073082.

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Many investigations use a linearization method, and others use a structural properties method to determine the controllability and observability of robots. In this study, we propose a transformed structural properties method to determine the controllability and observability of robots, which is the combination of the linearization and the structural properties methods. The proposed method uses a transformation in the robot model to obtain a linear robot model with the gravity terms and uses the linearization of the gravity terms to obtain the linear robot model; this linear robot model is used to determine controllability and observability. The described combination evades the structural conditions requirement and decreases the approximation error. The proposed method is better than previous methods because the proposed method can obtain more precise controllability and observability results. The modified structural properties method is compared with the linearization method to determine the controllability and observability of three robots.
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15

Vanderplaats, G. N., Y. J. Yang, and D. S. Kim. "Sequential linearization method for multilevel optimization." AIAA Journal 28, no. 2 (February 1990): 290–95. http://dx.doi.org/10.2514/3.10387.

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16

Leonov, G. A. "On the method of harmonic linearization." Automation and Remote Control 70, no. 5 (May 2009): 800–810. http://dx.doi.org/10.1134/s0005117909050087.

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17

Maeda, Takeo. "Linearization Method of Nonlinear Source Term." Transactions of the Japan Society of Mechanical Engineers Series B 59, no. 559 (1993): 827–32. http://dx.doi.org/10.1299/kikaib.59.827.

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18

Simulescu, Ion, Takashi Mochio, and Masanobu Shinozuka. "Equivalent Linearization Method IN NONLINEAR FEM." Journal of Engineering Mechanics 115, no. 3 (March 1989): 475–92. http://dx.doi.org/10.1061/(asce)0733-9399(1989)115:3(475).

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19

Danilin, Yu M. "Linearization method using modified lagrange functions." Cybernetics and Systems Analysis 30, no. 1 (January 1994): 80–94. http://dx.doi.org/10.1007/bf02366367.

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20

Pshenichnyi, B. N., and L. A. Sobolenko. "Linearization method for inverse convex programming." Cybernetics and Systems Analysis 31, no. 6 (November 1995): 852–62. http://dx.doi.org/10.1007/bf02366622.

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21

Ricciardi, Giuseppe. "A non-Gaussian stochastic linearization method." Probabilistic Engineering Mechanics 22, no. 1 (January 2007): 1–11. http://dx.doi.org/10.1016/j.probengmech.2006.04.001.

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22

Živanović, D. B., M. Z. Arsić, and J. R. Djordjević. "Two-Stage Piece-Wise Linearization Method." International Journal of Modelling and Simulation 24, no. 2 (January 2004): 85–89. http://dx.doi.org/10.1080/02286203.2004.11442291.

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23

Wang, Dini, Fanwei Meng, and Shengya Meng. "Linearization Method of Nonlinear Magnetic Levitation System." Mathematical Problems in Engineering 2020 (June 22, 2020): 1–5. http://dx.doi.org/10.1155/2020/9873651.

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Linearized model of the system is often used in control design. It is generally believed that we can obtain the linearized model as long as the Taylor expansion method is used for the nonlinear model. This paper points out that the Taylor expansion method is only applicable to the linearization of the original nonlinear function. If the Taylor expansion is used for the derived nonlinear equation, wrong results are often obtained. Taking the linearization model of the maglev system as an example, it is shown that the linearization should be carried out with the process of equation derivation. The model is verified by nonlinear system simulation in Simulink. The method in this paper is helpful to write the linearized equation of the control system correctly.
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24

Chang, R. J., and S. J. Lin. "Statistical Linearization Model for the Response Prediction of Nonlinear Stochastic Systems Through Information Closure Method." Journal of Vibration and Acoustics 126, no. 3 (July 1, 2004): 438–48. http://dx.doi.org/10.1115/1.1688762.

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A new linearization model with density response based on information closure scheme is proposed for the prediction of dynamic response of a stochastic nonlinear system. Firstly, both probability density function and maximum entropy of a nonlinear stochastic system are estimated under the available information about the moment response of the system. With the estimated entropy and property of entropy stability, a robust stability boundary of the nonlinear stochastic system is predicted. Next, for the prediction of response statistics, a statistical linearization model is constructed with the estimated density function through a priori information of moments from statistical data. For the accurate prediction of the system response, the excitation intensity of the linearization model is adjusted such that the response of maximum entropy is invariant in the linearization model. Finally, the performance of the present linearization model is compared and supported by employing two examples with exact solutions, Monte Carlo simulations, and Gaussian linearization method.
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25

Simanullang, Herlin, Sutarman Sutarman, and Open Darnius. "Simplifying Complexity: Linearization Method for Partial Least Squares Regression." SinkrOn 8, no. 3 (July 25, 2023): 1811–20. http://dx.doi.org/10.33395/sinkron.v8i3.12754.

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This research investigates Romera’s local linearization approach as a variance prediction method in partial least squares (PLS) regression. By addressing limitations in the original PLS regression formula, the local linearization approach aims to improve accuracy and stability in variance predictions. Extensive simulations are conducted to assess the method's performance, demonstrating its superiority over traditional algebraic methods and showcasing its computational advantages, particularly with a large number of predictors. Additionally, the study introduces a novel computational technique utilizing bootstrap parameters, enhancing computational stability and robustness. Overall, the research provides valuable insights into the local linearization approach's effectiveness, guiding researchers and practitioners in selecting more reliable and efficient regression modeling techniques.
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26

Li, Jin. "Barycentric Rational Collocation Method for Nonlinear Heat Conduction Equation." Journal of Applied Mathematics 2022 (June 30, 2022): 1–9. http://dx.doi.org/10.1155/2022/8998193.

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Nonlinear heat equation solved by the barycentric rational collocation method (BRCM) is presented. Direct linearization method and Newton linearization method are presented to transform the nonlinear heat conduction equation into linear equations. The matrix form of nonlinear heat conduction equation is also obtained. Several numerical examples are provided to valid our schemes.
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27

Geiser, Jürgen. "Modified Jacobian Newton Iterative Method: Theory and Applications." Mathematical Problems in Engineering 2009 (2009): 1–24. http://dx.doi.org/10.1155/2009/307298.

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This article proposes a new approach to the construction of a linearization method based on the iterative operator-splitting method for nonlinear differential equations. The convergence properties of such a method are studied. The main features of the proposed idea are the linearization of nonlinear equations and the application of iterative splitting methods. We present an iterative operator-splitting method with embedded Newton methods to solve nonlinearity. We confirm with numerical applications the effectiveness of the proposed iterative operator-splitting method in comparison with the classical Newton methods. We provide improved results and convergence rates.
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28

Bernard, Pierre, and Liming Wu. "Stochastic linearization: the theory." Journal of Applied Probability 35, no. 3 (September 1998): 718–30. http://dx.doi.org/10.1239/jap/1032265219.

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Very little is known about the quantitative behaviour of dynamical systems with random excitation, unless the system is linear. Known techniques imply the resolution of parabolic partial differential equations (Fokker–Planck–Kolmogorov equation), which are degenerate and of high dimension and for which there is no effective known method of resolution. Therefore, users (physicists, mechanical engineers) concerned with such systems have had to design global linearization techniques, known as equivalent statistical linearization (Roberts and Spanos (1990)). So far, there has been no rigorous justification of these techniques, with the notable exception of the paper by Kozin (1987). In this contribution, using large deviation principles, several mathematically founded linearization methods are proposed. These principles use relative entropy, or Kullback information, of two probability measures, and Donsker–Varadhan entropy of a Gaussian measure relatively to a Markov kernel. The method of ‘true linearization’ (Roberts and Spanos (1990)) is justified.
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29

Bernard, Pierre, and Liming Wu. "Stochastic linearization: the theory." Journal of Applied Probability 35, no. 03 (September 1998): 718–30. http://dx.doi.org/10.1017/s0021900200016363.

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Very little is known about the quantitative behaviour of dynamical systems with random excitation, unless the system is linear. Known techniques imply the resolution of parabolic partial differential equations (Fokker–Planck–Kolmogorov equation), which are degenerate and of high dimension and for which there is no effective known method of resolution. Therefore, users (physicists, mechanical engineers) concerned with such systems have had to design global linearization techniques, known as equivalent statistical linearization (Roberts and Spanos (1990)). So far, there has been no rigorous justification of these techniques, with the notable exception of the paper by Kozin (1987). In this contribution, using large deviation principles, several mathematically founded linearization methods are proposed. These principles use relative entropy, or Kullback information, of two probability measures, and Donsker–Varadhan entropy of a Gaussian measure relatively to a Markov kernel. The method of ‘true linearization’ (Roberts and Spanos (1990)) is justified.
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30

Živanović, Dragan, and Milan Simić. "Two-stage segment linearization as part of the thermocouple measurement chain." Measurement and Control 54, no. 1-2 (January 2021): 141–51. http://dx.doi.org/10.1177/0020294020986833.

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An implementation of a two-stage piece-wise linearization method for reduction of the thermocouple approximation error is presented in the paper. First, the whole thermocouple measurement chain of a transducer is described, and possible error is analysed to define the required level of accuracy for linearization of the transfer characteristics. Evaluation of linearization functions and analysis of approximation errors are performed by the virtual instrumentation software package LabVIEW. The method is appropriate for thermocouples and other sensors where nonlinearity varies a lot over the range of input values. The basic principle of this method is to first transform the abscissa of the transfer function by a linear segment look-up table in such a way that significantly nonlinear parts of the input range are expanded before a standard piece-wise linearization. In this way, applying equal-segment linearization two times has a similar effect to non-equal-segment linearization. For a given examples of the thermocouple transfer functions, the suggested method provides significantly better reduction of the approximation error, than the standard segment linearization, with equal memory consumption for look-up tables. The simple software implementation of this two-stage linearization method allows it to be applied in low calculation power microcontroller measurement transducers, as a replacement of the standard piece-wise linear approximation method.
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31

Igarashi, Yusuke, Masaki Yamakita, Jerry Ng, and H. Harry Asada. "A Robust Method for Dual Faceted Linearization." IFAC-PapersOnLine 53, no. 2 (2020): 6095–100. http://dx.doi.org/10.1016/j.ifacol.2020.12.1683.

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32

Elkhaldi, Said, Naima Amar Touhami, Mohamed Aghoutane, and Taj-Eddin Elhamadi. "LINC Method for MMIC Power Amplifier Linearization." Recent Advances in Electrical & Electronic Engineering (Formerly Recent Patents on Electrical & Electronic Engineering) 12, no. 5 (October 28, 2019): 402–7. http://dx.doi.org/10.2174/2352096511666180611101146.

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Background: This article proposes the design and implementation of a MMIC (monolithic microwave integrated circuits) Power amplifier using the ED02AH process. Methods: The MMIC ED02AH technology have been developed specifically for microwave applications up to millimeter waves, and for high-speed digital circuits. The use of a single branch of a power amplifier can produce high distortion. In the present paper, the Linear amplification with nonlinear components (LINC) method is introduced and applied as a solution to linearize the power amplifier, it can simultaneously provide high efficiency and high linearity. To validate the proposed approach, the design and characterization of a 5.25 GHz LINC Power Amplifier on MMIC technology is presented. Results: Good results have been achieved, and an improvement of about 37.50 dBc and 59 dBc respectively is obtained for the Δlower C/I and Δupper C/I at 5.25 GHz. Conclusion: As a result of this method, we can reduce the Carrier Power to Third-Order Intermodulation Distortion Power Ratio. Excellent linearization is obtained almost 37.6 dBc for Δlower C/I and 58.8 dBc for Δupper C/I.
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33

Lakshmi, P. Sri, and V. Lokesh Raju. "ECG De-noising using Hybrid Linearization Method." TELKOMNIKA Indonesian Journal of Electrical Engineering 15, no. 3 (September 1, 2015): 504. http://dx.doi.org/10.11591/tijee.v15i3.1568.

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<p>Electrocardiogram (ECG) is a non-invasive tool that monitors the electrical activity of the heart. An ECG signal is highly prone to the disturbances such as noise contamination, artifacts and other signals interference. So, an ECG signal has to be de-noised so that the distortions can be eliminated from the original signal for the perfect diagnosing of the condition and performance of the heart. Extended Kalman Filter (EKF) de-noises an ECG signal to some extent. This project proposes a method called Hybrid Linearization Method which is a combination of Extended Kalman Filter along with Discrete Wavelet Transform (DWT) resulting in an improved de-noised signal.</p>
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34

Mahadevan, Sankaran, and Pan Shi. "Multiple Linearization Method for Nonlinear Reliability Analysis." Journal of Engineering Mechanics 127, no. 11 (November 2001): 1165–73. http://dx.doi.org/10.1061/(asce)0733-9399(2001)127:11(1165).

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35

Robinson, Stephen M. "A Linearization Method for Nondegenerate Variational Conditions." Journal of Global Optimization 28, no. 3/4 (April 2004): 405–17. http://dx.doi.org/10.1023/b:jogo.0000026458.55147.46.

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36

Maeda, Takeo. "Numerical Linearization Method of Nonlinear Sourse Term." Transactions of the Japan Society of Mechanical Engineers Series B 59, no. 561 (1993): 1553–58. http://dx.doi.org/10.1299/kikaib.59.1553.

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37

Darania, P., A. Ebadian, and A. V. Oskoi. "Linearization method for solving nonlinear integral equations." Mathematical Problems in Engineering 2006 (2006): 1–10. http://dx.doi.org/10.1155/mpe/2006/73714.

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The objective of this paper is to assess both the applicability and the accuracy of linearization method in several problems of general nonlinear integral equations. This method provides piecewise linear integral equations which can be easily integrated. It is shown that the accuracy of linearization method can be substantially improved by employing variable steps which adjust themselves to the solution. This approach can reveal that, under this method, the nonlinear integral equations can be transformed into the linear integral equations which may be integrated using classical methods. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.
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38

Kajikawa, Yoshinobu. "Linearization method based on multiple loudspeaker systems." Acoustical Science and Technology 32, no. 5 (2011): 220–23. http://dx.doi.org/10.1250/ast.32.220.

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39

Pshenichnyi, B. N., and K. V. Nashempa. "Linearization method for constrained limit extremal problems." Cybernetics and Systems Analysis 28, no. 6 (November 1992): 905–11. http://dx.doi.org/10.1007/bf01291294.

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40

Rouff, Marc, and Matthieu Verdier. "Trajectories generation under constraints by linearization method." Computer Methods in Applied Mechanics and Engineering 154, no. 3-4 (March 1998): 179–91. http://dx.doi.org/10.1016/s0045-7825(97)00122-9.

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41

Ji-huan, He. "Linearization and correction method for nonlinear problems." Applied Mathematics and Mechanics 23, no. 3 (March 2002): 241–48. http://dx.doi.org/10.1007/bf02438331.

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42

Vlysidis, Michail, and Yiannis N. Kaznessis. "A linearization method for probability moment equations." Computers & Chemical Engineering 112 (April 2018): 1–5. http://dx.doi.org/10.1016/j.compchemeng.2018.01.015.

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43

Shcherbina, Yu N., and B. M. Golub. "Quasi-Newton modification of the linearization method." Cybernetics 24, no. 6 (1989): 759–66. http://dx.doi.org/10.1007/bf01079149.

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44

Hurtado, Jorge E., and Alex H. Barbat. "Improved stochastic linearization method using mixed distributions." Structural Safety 18, no. 1 (January 1996): 49–62. http://dx.doi.org/10.1016/0167-4730(96)00017-3.

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45

Samuelsson, Pär, Hans Norlander, and Bengt Carlsson. "An integrating linearization method for Hammerstein models." Automatica 41, no. 10 (October 2005): 1825–28. http://dx.doi.org/10.1016/j.automatica.2005.04.018.

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46

Shaoqian, Zhou, Ding Lixin, Zhang Jian, and Tang Xinhua. "Linearization learning method of BP neural networks." Wuhan University Journal of Natural Sciences 2, no. 1 (March 1997): 35–39. http://dx.doi.org/10.1007/bf02834910.

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47

Mohos, Ferenc Á., and Eszter Vozáry. "Evaluation of relaxation and creep curve by application of peleg linearization and prony series." Progress in Agricultural Engineering Sciences 14, no. 1 (December 2018): 61–75. http://dx.doi.org/10.1556/446.14.2018.1.3.

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In practice, there is a demand for quick characterization of rheological properties of food materials. The exact model calculation requires complex and long-term mathematical process. In this work, a simple, quick linearization method – the Peleg linearization – is discussed and is compared with the Prony series method. In the Peleg linearization only two constants are used, one of them gives the initial rate of relaxation or creep and the second one gives the equilibrium value of relaxing force or of creeping strain. The Prony series approach the relaxation and creep with the sum of two or more exponential functions and equilibrium values. Both methods give the same equilibrium values for both the relaxation and creep of wine gums and apple. The initial increasing rate of creep is higher by the Peleg linearization and lower by the Prony series. At relaxation the initial decreasing rate is lower by the Peleg linearization and higher by the Prony series.
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48

Savochkin, V. A., and S. M. Shishanov. "Relation Between Features of Harmonic Statistical Linearization." Izvestiya MGTU MAMI 1, no. 2 (January 20, 2007): 99–105. http://dx.doi.org/10.17816/2074-0530-69600.

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The paper presents the basic computations of method of combined linearization of elastic and damping performance of transport machine cushioning system. This method may be realized if the harmonic linearization coefficient of cushioning system are preliminary determined. This method is based on the possibility to present the differentiable random stationary process as a harmonic signal randomly modulated by phase and amplitude; if relational motion of track roller is a differentiable stationary process, it may be presented as a centered harmonic oscillation. The paper argues that the method of combined linearization is effective if analytical (and graphical) expressions for equivalent coefficients of harmonic linearization are already known.
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49

Socha, L. "Linearization in Analysis of Nonlinear Stochastic Systems: Recent Results—Part I: Theory." Applied Mechanics Reviews 58, no. 3 (May 1, 2005): 178–205. http://dx.doi.org/10.1115/1.1896368.

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The purpose of Part 1 of this paper is to provide a review of recent results from 1991 through 2003 in the area of theoretical aspects of statistical and equivalent linearization in the analysis of structural and mechanical nonlinear stochastic dynamic systems. First, a discussion about misunderstandings appearing in the literature in derivation of linearization coefficients for mean-square linearization criterion is presented. In Secs. 3–6 new theoretical results, including new types of criteria, nonlinearities, and excitations in the context of linearization methods, are reviewed. In particular, moment criteria called energy criteria, linearization criteria in the space of power spectral density functions and probability density functions are discussed. A survey of a wide class of so-called nonlinearization techniques, including equivalent quadratization and equivalent cubicization methods, is given in Sec. 7. New linearization techniques for nonlinear stochastic systems with parametric Gaussian excitations and external non-Gaussian excitations are discussed in Secs. 8 and 9, respectively. In the last sections, four surveys of papers where stochastic linearization is used as a mathematical tool in other theoretical approaches, namely, models of dynamic systems with hysteresis, finite element method, and control of nonlinear stochastic systems and linearization with sensitivity analysis, are given. A discussion of the accuracy analysis of linearization techniques and some general conclusions close this paper. There are 217 references cited in this revised article.
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Atanaskovic, Aleksandar, Natasa Males-Ilic, Aleksandra Djoric, and Djuradj Budimir. "Doherty amplifier linearization by digital injection methods." Facta universitatis - series: Electronics and Energetics 35, no. 4 (2022): 587–601. http://dx.doi.org/10.2298/fuee2204587a.

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Abstract:
Verification of two linearization methods, applied on asymmetrical two-way microstrip Doherty amplifier in experiment and on symmetrical two-way Doherty amplifier in simulation, is performed in this paper. The laboratory set-ups are formed to generate the baseband nonlinear linearization signals of the second-order. After being tuned in magnitude and phase in the digital domain the linearization signals modulate the second harmonics of fundamental carrier. In the first method, adequately processed signals are then inserted at the input and output of the main Doherty amplifier transistor, whereas in the second method, they are injected at the outputs of the Doherty main and auxiliary amplifier transistors. The experimental results are obtained for 64QAM digitally modulated signals. As a proof of concept, the linearization methods are also verified in simulation, for Doherty amplifier designed to work in 5G band below 6 GHz, utilizing 20 MHz LTE signal.
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