• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.305-320
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• 2020

This study aims to generalize MINRES-N2 method [1]. It means that we tend to obtain an algorithm to transfer each normal matrix - that its eigenvalues belong to an algebraic curve of low degree k- to its condensed form through using a unitary similarity transformation. Then, we aim to obtain a method to solve a system of linear equations that its coefficient matrix is equal to such a matrix by utilizing it. Finally this method is compared to the well-known GMRES method through using numerical examples. The results obtained through examples show that the given method is more efficient than GMRES.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.375-388
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• 2004

For solving symmetric systems of linear equations, it is shown that a new Krylov subspace method can be obtained. The new approach is one of the projection methods, and we call it the projection method for convenience in this paper. The projection method maintains the residual vector like simpler GMRES, symmetric QMR, SYMMLQ, and MINRES. By studying the quasiminimal residual method, we show that an extended projection method and the scaled symmetric QMR method are equivalent.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.29-36
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• 1999

It is shown that a new Krylov subspace method for solving symmetric indefinite systems of linear equations can be obtained. We call the method as the projection method in this paper. The residual vector of the projection method is maintained at each iteration, which may be useful in some applications.