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Relevant bibliographies by topics / Karhunen-Loeve expansion

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Journal articles

Academic literature on the topic 'Karhunen-Loeve expansion'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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Journal articles on the topic "Karhunen-Loeve expansion"

1

Paff, W. G., and G. Ahmadi. "On the Convergence of Karhunen-Loeve Series Expansion for a Brownian Particle." Journal of Applied Mechanics 60, no. 3 (1993): 783–84. http://dx.doi.org/10.1115/1.2900876.

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A linear Langevin equation for the velocity of a Brownian particle is considered. The equation of motion is solved and the Karhunen-Loeve expansion for the particle velocity is derived. The mean-square velocity as obtained by the truncated Karhunen-Loeve expansion is compared with the exact solution. It is shown, as the number of terms in the series increases, the result approaches that of the exact solution asymptotically.

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2

BABUŠKA, IVO, and KANG-MAN LIU. "ON SOLVING STOCHASTIC INITIAL-VALUE DIFFERENTIAL EQUATIONS." Mathematical Models and Methods in Applied Sciences 13, no. 05 (2003): 715–45. http://dx.doi.org/10.1142/s0218202503002696.

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This paper addresses the issues involved in solving systems of linear ODE's with stochastic coefficients and loadings described by the Karhunen–Loeve expansion. The Karhunen–Loeve expansion is used to discretize random functions into a denumerable set of uncorrelated random variables, thus providing us for transforming this problem into an equivalent deterministic one. Perturbation error estimates and a priori error estimates between the exact solution and the finite element solution in the framework of Sobolev space are given. The method of successive approximations for finite element solutio

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3

Courmontagne, Ph. "A new formulation for the Karhunen–Loeve expansion." Signal Processing 79, no. 3 (1999): 235–49. http://dx.doi.org/10.1016/s0165-1684(99)00099-7.

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4

Jaimez, Ramón Gutiérrez, and Mariano J. Valderrama Bonnet. "On the Karhunen-Loeve expansion for transformed processes." Trabajos de Estadistica 2, no. 2 (1987): 81–90. http://dx.doi.org/10.1007/bf02863594.

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5

Li, Heng. "Conditional Simulation of Flow in Heterogeneous Porous Media with the Probabilistic Collocation Method." Communications in Computational Physics 16, no. 4 (2014): 1010–30. http://dx.doi.org/10.4208/cicp.090513.040414a.

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AbstractA stochastic approach to conditional simulation of flow in randomly heterogeneous media is proposed with the combination of the Karhunen-Loeve expansion and the probabilistic collocation method (PCM). The conditional log hydraulic conductivity field is represented with the Karhunen-Loeve expansion, in terms of some deterministic functions and a set of independent Gaussian random variables. The propagation of uncertainty in the flow simulations is carried out through the PCM, which relies on the efficient polynomial chaos expansion used to represent the flow responses such as the hydrau

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6

Phoon, K. K., S. P. Huang, and S. T. Quek. "Simulation of second-order processes using Karhunen–Loeve expansion." Computers & Structures 80, no. 12 (2002): 1049–60. http://dx.doi.org/10.1016/s0045-7949(02)00064-0.

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7

Hilai, Ran, and Jacob Rubinstein. "Recognition of rotated images by invariant Karhunen–Loeve expansion." Journal of the Optical Society of America A 11, no. 5 (1994): 1610. http://dx.doi.org/10.1364/josaa.11.001610.

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8

Smallwood, David. "Characterization and Simulation of Gunfire with Karhunen-Loeve Expansion." Journal of the IEST 47, no. 1 (2004): 47–50. http://dx.doi.org/10.17764/jiet.47.1.3476326r02g27247.

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Gunfire is used as an example to illustrate how the Karhunen-Loeve (K-L) expansion can be used to characterize and simulate nonstationary random events. This paper will develop a method to describe the nonstationary random process in terms of a K-L expansion. The gunfire record is broken up into a sequence of transient waveforms, each representing the response to the firing of a single round. First, the mean is estimated and subtracted from each waveform. The mean is an estimate of the deterministic part of the gunfire. The autocovariance matrix is estimated from the matrix of these single-rou

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9

Ai, Xiaohui. "Karhunen–Loeve expansion for the additive detrended Brownian motion." Communications in Statistics - Theory and Methods 46, no. 16 (2016): 8210–16. http://dx.doi.org/10.1080/03610926.2016.1177079.

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10

Lenz, Reiner, and Mats Österberg. "Computing the Karhunen-Loeve Expansion with a Parallel, Unsupervised Filter System." Neural Computation 4, no. 3 (1992): 382–92. http://dx.doi.org/10.1162/neco.1992.4.3.382.

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We use the invariance principle and the principles of maximum information extraction and maximum signal concentration to design a parallel, linear filter system that learns the Karhunen-Loeve expansion of a process from examples. In this paper we prove that the learning rule based on these principles forces the system into stable states that are pure eigenfunctions of the input process.

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