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Recently, two efficient algorithms for solving comrade linear systems have been proposed by Karawia [A.A. Karawia, Two algorithms for solving comrade linear systems, Appl. Math. Comput. 189 (2007) 291–297]. The two algorithms are based on the LU decomposition of the comrade matrix. In this paper, two algorithms are presented for solving the comrade linear(More)
Keywords: k-tridiagonal matrix Block diagonalizations Generalized k-Fibonacci numbers Determinant Finite field General linear group a b s t r a c t In the present paper, we give a fast algorithm for block diagonalization of k-tridiagonal matrices. The block diagonalization provides us with some useful results: e.g., another derivation of a very recent(More)
In this paper, we consider an inverse problem with the k-tridiagonal Toeplitz matrices. A theoretical result is obtained that under certain assumptions the explicit inverse of a k-tridiagonal Toeplitz matrix can be derived immediately. Two numerical examples are given to demonstrate the validity of our results. (c) ٢٠١٢ Elsevier Ltd. All rights reserved.(More)
A linear algebraic theory called the 'multiple Arnoldi method' is presented and realizes large-scale (order-N) electronic structure calculations with generalized eigenvalue equations. A set of linear equations, in the form of (zS - H)x = b, are solved simultaneously with multiple Krylov subspaces. The method is implemented in a simulation package ELSES(More)