Results 1 to 10 of about 180,323 (177)
Regularization matrices for discrete ill-posed problems in several space-dimensions [PDF]
Numerical Linear Algebra with Applications, 2017 Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space dimensions.
Dykes, L. +3 more
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Fractional regularization matrices for linear discrete ill-posed problems [PDF]
Journal of Engineering Mathematics, 2015 The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices
Lothar Reichel +2 more
core +6 more sources
On the discrete linear ill‐posed problems
Mathematical Modelling and Analysis, 1999 An inverse problem of photo‐acoustic spectroscopy of semiconductors is investigated. The main problem is formulated as the integral equation of the first kind.
A. A. Stepanov
doaj +5 more sources
Modified Truncated Randomized Singular Value Decomposition (MTRSVD) Algorithms for Large Scale Discrete Ill-posed Problems with General-Form Regularization [PDF]
, 2018 In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: ${\min} \|Lx\|$ subject to ${\min} \|Ax - b\|$, where $L$ is a regularization matrix.
Jia, Zhongxiao, Yang, Yanfei
core +2 more sources
Range restricted iterative methods for linear discrete ill-posed problems
ETNA - Electronic Transactions on Numerical Analysis, 2023 . Linear systems of equations with a matrix whose singular values decay to zero with increasing index number, and without a significant gap, are commonly referred to as linear discrete ill-posed problems.
A. Buccini, Lucas Onisk, L. Reichel
semanticscholar +2 more sources
Fractional Tikhonov regularization for linear discrete ill-posed problems [PDF]
BIT Numerical Mathematics, 2011 Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The
M. Hochstenbach, L. Reichel
semanticscholar +6 more sources
Numerical Algorithms, 2019 For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by Gaussian white noise, there are four commonly used Krylov solvers: LSQR and its mathematically equivalent CGLS, the Conjugate Gradient (CG) method ...
Jia, Zhongxiao
core +2 more sources
Vector Extrapolation Based Landweber Method for Discrete Ill-Posed Problems [PDF]
Mathematical Problems in Engineering, 2017 Landweber method is one of the classical iterative methods for solving linear discrete ill-posed problems. However, Landweber method generally converges very slowly.
Xile Zhao +3 more
semanticscholar +4 more sources
Global Golub-Kahan bidiagonalization applied to large discrete ill-posed problems
Journal of Computational and Applied Mathematics, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Bentbib +3 more
semanticscholar +3 more sources
Randomized core reduction for discrete ill-posed problem [PDF]
Journal of Computational and Applied Mathematics, 2020 In this paper, we apply randomized algorithms to approximate the total least squares (TLS) solution of the problem $Ax\approx b$ in the large-scale discrete ill-posed problems. A regularization technique, based on the multiplicative randomization and the subspace iteration, is proposed to obtain the approximate core problem.In the error analysis, we ...
Liping Zhang, Yimin Wei
openaire +2 more sources