What is it about?
In this study two classes of high order methods for the approximate matrix inversion are given. Methods with convergence orders p=7,13 from Class 1 and methods with convergence orders p=9,19 from Class 2 are used to obtain polynomial preconditioners for preconditioning the BICG method for solving well-posed and ill-posed problems. Numerical comparisons with other existing polynomial preconditioners are provided.
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Why is it important?
It is shown that BICG method converges very quickly when applied to solve the preconditioned linear system. Therefore, the cost of constructing these preconditioners is amortized if the preconditioner is to be reused over several systems of same coefficient matrix with different right sides.
Perspectives
Writing this article was a great motivation and I hope it leads to greater involvement in the field of preconditioning methods.
Suzan Cival Buranay
Eastern Mediterranean University
Read the Original
This page is a summary of: On the two classes of high-order convergent methods of approximate inverse preconditioners for solving linear systems, Numerical Linear Algebra with Applications, June 2017, Wiley,
DOI: 10.1002/nla.2111.
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