Numerical aspects of gram-schmidt orthogonalization of vectors
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TLDR
Several variants of Gram-Schmidt orthogonalization are reviewed from a numerical point of view in this paper, and it is shown that the classical and modified variants correspond to the Gauss-Jacobi and Gauss -Seidel iterations for linear systems.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-07-01 and is currently open access. It has received 73 citations till now. The article focuses on the topics: Orthogonalization & Gram–Schmidt process.read more
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Accelerated Randomized Coordinate Descent for Solving Linear Systems
TL;DR: In this paper , the Nesterov accelerated randomized coordinate descent (NARCD) method is proposed to accelerate the RCD method by choosing a proper momentum parameter, and the global convergence rates of the two methods are established.
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Augmented Block-Arnoldi Recycling CFD Solvers
TL;DR: In this paper , an inverse compact modified Gram-Schmidt algorithm is applied for the inter-block orthogonalization scheme with a block lower triangular correction matrix at iteration $k$ when combined with a weighted (oblique inner product) projection step, the inverse compact $WY$ scheme leads to significant reduction in the number of solver iterations per linear system.
References
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Matrix iterative analysis
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
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LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
TL;DR: Numerical tests are described comparing I~QR with several other conjugate-gradient algorithms, indicating that I ~QR is the most reliable algorithm when A is ill-conditioned.
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Numerical methods for solving linear least squares problems
TL;DR: This paper considers stable numerical methods for handling linear least squares problems that frequently involve large quantities of data, and they are ill-conditioned by their very nature.
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Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
TL;DR: This work was supported by Natural Sciences and Engineering Research Council of Canada Grant A8652, by the New Zealand Department of Scientific and Industrial Research, and by the Department of Energy under Contract DE-AT03-76ER72018.