Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices

DOI10.1137/18M1218212zbMath1434.65041arXiv1809.11085MaRDI QIDQ5220401

Yusaku Yamamoto, Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yuka Yanagisawa

Publication date: 20 March 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.11085

zbMATH Keywords

roundoff error analysisQR factorizationcommunication-avoiding algorithmsCholesky QR factorizationoblique inner product

Mathematics Subject Classification ID

Factorization of matrices (15A23) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Eigenvalues, singular values, and eigenvectors (15A18) Roundoff error (65G50)

Related Items

Mixed precision algorithms in numerical linear algebra ⋮ Householder Orthogonalization with a Nonstandard Inner Product ⋮ Exact QR factorizations of rectangular matrices ⋮ The Stability of Block Variants of Classical Gram--Schmidt ⋮ Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices ⋮ Block Gram-Schmidt algorithms and their stability properties ⋮ Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems

Uses Software

• JDQR
• SparseMatrix
• mctoolbox
• JDQZ
• CholQR
• CholeskyQR2

Cites Work

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