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Abstract
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In this paper, a new block preconditioner is proposed for the block partitioned matrices.
This preconditioner is based on the block C-orthogonalization, where C is a symmetric positive definite matrix. The block preconditioned least squares (BPLS) and block preconditioned global least squares (BPGLS) algorithms are presented to solve the linear system
of equations with block partioned coefficient matrix and multiple linear system of equations, respectively. The BPLS algorithm is applied to solve the complex linear system of
equations and also BPLS and classical preconditioned least squares (PLS) algorithms are
compared. Finally, some numerical experiments are given to show the efficiency of the
new block preconditioner.
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