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TRIDIAGONALITY OF J-NORMAL AND J-CONJUGATE NORMAL HESSENBERG MATRICES
M. GHASEMI KAMALVAND,K. NIAZIASIL 한국산업응용수학회 2020 Journal of the Korean Society for Industrial and A Vol.24 No.1
In this parer we express the sufficient conditions under which it is proved that a J-normal irreduciable Hessenberg matrix is tridiagonal and it is also proved that a similar statement exists for J-conjugate normal matrices.
A METHOD FOR SOLVING OF LINEAR SYSTEM WITH NORMAL COEFFICIENT MATRICES
M. GHASEMI KAMALVAND,B.FARAZMANDNIA,M.ALIYARI 한국산업응용수학회 2020 Journal of the Korean Society for Industrial and A Vol.24 No.3
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.
ON REDUCTION OF K-ALMOST NORMAL AND K-ALMOST CONJUGATE NORMAL MATRICES TO A BLOCK TRIDIAGONAL FORM
K. NIAZI ASIL,M. GHASEMI KAMALVAND 한국산업응용수학회 2019 Journal of the Korean Society for Industrial and A Vol.23 No.3
This paper examines how one can build a block tridiagonal structure for k-almost normal matrices and also for k-almost conjugate normal matrices. We shall see that these representations are created by unitary similarity and unitary congruance transformations, respectively. It shall be proven that the orders of diagonal blocks are 1, k + 2, 2k + 3, ..., in both cases. Then these block tridiagonal structures shall be reviewed for the cases where the mentioned matrices satisfy in a second-degree polynomial. Finally, for these processes, algorithms are presented.