Solution of large‐scale weighted least‐squares problems | Zendy

Baryamureeba Venansius | Zendy

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Solution of large‐scale weighted least‐squares problems

Author(s) -

Baryamureeba Venansius

Publication year - 2002

Publication title -

numerical linear algebra with applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.02

H-Index - 53

eISSN - 1099-1506

pISSN - 1070-5325

DOI - 10.1002/nla.232

Subject(s) - solver , mathematics , rank (graph theory) , least squares function approximation , positive definite matrix , matrix (chemical analysis) , diagonal , linear least squares , sequence (biology) , scale (ratio) , combinatorics , boundary value problem , algorithm , mathematical optimization , mathematical analysis , singular value decomposition , geometry , statistics , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , estimator , biology , composite material , genetics

A sequence of least‐squares problems of the form min y ∥ G 1/2 ( A T y − h )∥ 2 , where G is an n × n positive‐definite diagonal weight matrix, and A an m × n ( m ⩽ n ) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We suggest low‐rank correction preconditioners for such problems, and a mixed solver (a combination of a direct solver and an iterative solver). The numerical results show that our technique for selecting the low‐rank correction matrix is very effective. Copyright © 2002 John Wiley & Sons, Ltd.

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