Abstract
Continuing from the works of Li et al. (2014), Li (2007), and Kincaid et al. (2000), we present more generalizations and modifications of iterative methods for solving large sparse symmetric and nonsymmetric indefinite systems of linear equations. We discuss a variety of iterative methods such as GMRES, MGMRES, MINRES, LQ-MINRES, QR MINRES, MMINRES, MGRES, and others.
Highlights
When solving large sparse linear systems of the form Ax = b, 2
Using (6), (7), and (5), we expand the coefficient matrix on the left-hand side of linear system (18)
We find that the coefficient matrix (26) can be written as we are interested in solving this linear system (LnLTn + σn2eneTn ) y(n) = σ0Tne1
Summary
We assume that matrix A is symmetric. W(n−3), w(n−2), w(n−1)} as follows: in which the coefficient matrix A is indefinite, there are basis methods and a variety of generalizations and modifications of them. Basic iterative methods for symmetric indefinite linear systems are the MINRES method and the SYMMLQ method, while a basic method for nonsymmetric linear systems is the GMRES method.
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