The Stability of Block Variants of Classical Gram-Schmidt

The block version of the classical Gram--Schmidt (\tt BCGS) method is often employed to efficiently compute orthogonal bases for Krylov subspace methods and eigenvalue solvers, but a rigorous proof...

[1]  Yusaku Yamamoto,et al.  Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices , 2018, SIAM J. Sci. Comput..

[2]  E. Haynsworth Determination of the inertia of a partitioned Hermitian matrix , 1968 .

[3]  L. Reichel,et al.  A Newton basis GMRES implementation , 1994 .

[4]  JESSE L. BARLOW,et al.  Block Modified Gram-Schmidt Algorithms and Their Analysis , 2019, SIAM J. Matrix Anal. Appl..

[5]  Julien Langou,et al.  A note on the error analysis of classical Gram–Schmidt , 2006, Numerische Mathematik.

[6]  N. Abdelmalek Round off error analysis for Gram-Schmidt method and solution of linear least squares problems , 1971 .

[7]  James Demmel,et al.  Stability of block LU factorization , 1992, Numer. Linear Algebra Appl..

[8]  Jesse L. Barlow,et al.  Reorthogonalized block classical Gram–Schmidt , 2011, Numerische Mathematik.

[9]  Kirk M. Soodhalter,et al.  Admissible and attainable convergence behavior of block Arnoldi and GMRES , 2019, SIAM J. Matrix Anal. Appl..

[10]  Jack J. Dongarra,et al.  Mixed-Precision Cholesky QR Factorization and Its Case Studies on Multicore CPU with Multiple GPUs , 2015, SIAM J. Sci. Comput..

[11]  Laura Grigori,et al.  Enlarged Krylov Subspace Conjugate Gradient Methods for Reducing Communication , 2016, SIAM J. Matrix Anal. Appl..

[12]  Julien Langou,et al.  Rounding error analysis of the classical Gram-Schmidt orthogonalization process , 2005, Numerische Mathematik.

[13]  William Jalby,et al.  Stability Analysis and Improvement of the Block Gram-Schmidt Algorithm , 1991, SIAM J. Sci. Comput..

[14]  W. Joubert,et al.  Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory , 1992 .

[15]  Å. Björck Solving linear least squares problems by Gram-Schmidt orthogonalization , 1967 .