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Factored Inverses of Real Symmetric Matrices

Jane Cullum, Ralph A. Willoughby

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Abstract

The FORTRAN codes in this chapter address the question of computing distinct eigenvalues and corresponding eigenvectors of a real symmetric matrix by applying a single-vector Lanczos procedure to the inverse of an associated matrix B ≡ PCPT, where C = S0*A + SHIFT*I. The scalars S0 and SHIFT are specified by the user, selected in such a way that the resulting matrix C (or B) has a reasonable numerical condition. The permutation matrix P is chosen so that for a sparse matrix A, the resulting factorization of B is also sparse.

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What this paper is about

The FORTRAN codes in this chapter address the question of computing distinct eigenvalues and corresponding eigenvectors of a real symmetric matrix by applying a single-vector Lanczos procedure to the inverse of an associated matrix B ≡ PCPT, where C = S0*A + SHIFT*I. The scalars S0 and SHIFT are specified by the user, selected in such a way that the resulting matrix C (or B) has a reasonable numerical condition. The permutation matrix P is chosen so that for a sparse matrix A, the resulting factorization of B is also sparse.

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Available abstract

The FORTRAN codes in this chapter address the question of computing distinct eigenvalues and corresponding eigenvectors of a real symmetric matrix by applying a single-vector Lanczos procedure to the inverse of an associated matrix B ≡ PCPT, where C = S0*A + SHIFT*I. The scalars S0 and SHIFT are specified by the user, selected in such a way that the resulting matrix C (or B) has a reasonable numerical condition. The permutation matrix P is chosen so that for a sparse matrix A, the resulting factorization of B is also sparse.

Key concepts: Eigenvalues and eigenvectors, Symmetric matrix, Matrix (chemical analysis), Mathematics, Permutation matrix, Sparse matrix, Centrosymmetric matrix, Inverse

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