Cholesky decomposition of the Hilbert matrix
Copyright policy )Cholesky decomposition of the Hilbert matrix
The paper deals with a modified Cholesky decomposition \(H=LDL\) T, of the Hilbert matrix \(H=[1/(j+k-1)],\) where L is lower triangular with diagonal elements being 1, D is diagonal, L T is the transpose of L. Precise formulas for the Cholesky components L, D and the inverse \(L^{-1}\) are given. The formulas obtained are modified in such a way that the Hilbert matrix has a representation \(H=E^{-1}RGR\quad TE^{-1},\) where G, R, E have only integer entries.
Hilbert matrix, Hermitian, skew-Hermitian, and related matrices, Direct numerical methods for linear systems and matrix inversion, Cholesky decomposition, Factorization of matrices
Hilbert matrix, Hermitian, skew-Hermitian, and related matrices, Direct numerical methods for linear systems and matrix inversion, Cholesky decomposition, Factorization of matrices
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