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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)
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)