[BOOK][B] Numerical methods for least squares problems
Å Björck - 2024 - SIAM
Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …
1996. Least squares and least-norm problems have become more significant with every …
A survey of numerical linear algebra methods utilizing mixed-precision arithmetic
The efficient utilization of mixed-precision numerical linear algebra algorithms can offer
attractive acceleration to scientific computing applications. Especially with the hardware …
attractive acceleration to scientific computing applications. Especially with the hardware …
Block Gram-Schmidt algorithms and their stability properties
Abstract Block Gram-Schmidt algorithms serve as essential kernels in many scientific
computing applications, but for many commonly used variants, a rigorous treatment of their …
computing applications, but for many commonly used variants, a rigorous treatment of their …
The state of software for evolutionary biology
Abstract With Next Generation Sequencing data being routinely used, evolutionary biology
is transforming into a computational science. Thus, researchers have to rely on a growing …
is transforming into a computational science. Thus, researchers have to rely on a growing …
Fast and stable randomized low-rank matrix approximation
Y Nakatsukasa - arxiv preprint arxiv:2009.11392, 2020 - arxiv.org
Randomized SVD has become an extremely successful approach for efficiently computing a
low-rank approximation of matrices. In particular the paper by Halko, Martinsson, and Tropp …
low-rank approximation of matrices. In particular the paper by Halko, Martinsson, and Tropp …
Krylov methods for nonsymmetric linear systems
G Meurant, JD Tebbens - Cham: Springer, 2020 - Springer
Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …
Reorthogonalized block classical Gram–Schmidt using two Cholesky-based TSQR algorithms
JL Barlow - SIAM Journal on Matrix Analysis and Applications, 2024 - SIAM
In [Numer. Math., 23 (2013), pp. 395–423], Barlow and Smoktunowicz propose the
reorthogonalized block classical Gram–Schmidt algorithm BCGS2. New conditions for the …
reorthogonalized block classical Gram–Schmidt algorithm BCGS2. New conditions for the …
Shifted Cholesky QR for computing the QR factorization of ill-conditioned matrices
The Cholesky QR algorithm is an efficient communication-minimizing algorithm for
computing the QR factorization of a tall-skinny matrix X∈R^m*n, where m≫n. Unfortunately …
computing the QR factorization of a tall-skinny matrix X∈R^m*n, where m≫n. Unfortunately …
Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems
NJ Higham, S Pranesh - SIAM Journal on Scientific Computing, 2021 - SIAM
What is the fastest way to solve a linear system Ax=b in arithmetic of a given precision when
A is symmetric positive definite and otherwise unstructured? The usual answer is by …
A is symmetric positive definite and otherwise unstructured? The usual answer is by …
A robust and efficient implementation of LOBPCG
Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to
compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from …
compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from …