Solution of sparse rectangular systems using LSQR and CRAIG | Zendy

Michael A. Saunders | Zendy

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Solution of sparse rectangular systems using LSQR and CRAIG

Author(s) -

Michael A. Saunders

Publication year - 1995

Publication title -

bit numerical mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.904

H-Index - 59

eISSN - 1572-9125

pISSN - 0006-3835

DOI - 10.1007/bf01739829

Subject(s) - residual , regularization (linguistics) , mathematics , linear system , extension (predicate logic) , least squares function approximation , iterative method , system of linear equations , matrix (chemical analysis) , algorithm , sparse matrix , mathematical optimization , computer science , mathematical analysis , artificial intelligence , statistics , materials science , physics , quantum mechanics , estimator , composite material , gaussian , programming language

We examine two iterative methods for solving rectangular systems of linear equations: LSQR for over-determined systemsAx ˜ b, and Craig's method for under-determined systemsAx = b. By including regularization, we extend Craig's method to incompatible systems, and observe that it solves the same damped least-squares problems as LSQR. The methods may therefore be compared on rectangular systems of arbitrary shape.

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