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Julia and Singularity for High Performance Computing Read chapter Read first chapter

2021 | OriginalPaper | Chapter

A Note on the Sensitivity of Generic Approximate Sparse Pseudoinverse Matrix for Solving Linear Least Squares Problems

Authors : A. D. Lipitakis, G. A. Gravvanis, C. K. Filelis-Papadopoulos, D. Anagnostopoulos

Published in: Advances in Parallel & Distributed Processing, and Applications

Publisher: Springer International Publishing

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Abstract

During the last decades, research efforts have been focused on the derivation of effective explicit preconditioned iterative methods. In this manuscript, we review the Explicit Preconditioned Conjugate Gradient Least Squares method, based on generic sparse approximate pseudoinverses, in conjunction with approximate pseudoinverse sparsity patterns, based on the modified row-threshold incomplete QR factorization techniques. Additionally, modified Moore-Penrose conditions are presented, and theoretical estimates for the sensitivity of the generic approximate sparse pseudoinverses are derived. Finally, numerical results concerning the generic approximate sparse pseudoinverses by solving characteristic model problems are given. The theoretical estimates were in qualitative agreement with the numerical results.

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Metadata
Title
A Note on the Sensitivity of Generic Approximate Sparse Pseudoinverse Matrix for Solving Linear Least Squares Problems
Authors
A. D. Lipitakis
G. A. Gravvanis
C. K. Filelis-Papadopoulos
D. Anagnostopoulos
Copyright Year
2021
Book
Advances in Parallel & Distributed Processing, and Applications

Print ISBN: 978-3-030-69983-3

Electronic ISBN: 978-3-030-69984-0

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-69984-0_21