Learn More
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)
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)
Keywords: Elementary symmetric polynomials Complete symmetric polynomials Power sum symmetric polynomials Matrices Determinant LU factorization Stirling numbers a b s t r a c t This paper presents some applications using several properties of three important symmetric polynomials: elementary symmetric polynomials, complete symmetric polynomials and the(More)