Cholesky-like Factorizations of Skew-symmetric Matrices
نویسندگان
چکیده
As will be shown in this paper, there always exists an R such that (1.1) holds. We present a stable O(n3) algorithm that computes an R that has the form of a permuted triangular matrix. Our motivation comes from eigenvalue problems with Hamiltonian structure. A matrix H ∈ R is said to be Hamiltonian if (JH) = JH and skew-Hamiltonian if (JH) = −JH . EXAMPLE 1. The study of corner singularities in anisotropic elastic materials [5, 6, 11, 9] leads to generalized eigenvalue problems of the form
منابع مشابه
A SYM-ILDL: Incomplete LDL Factorization of Symmetric Indefinite and Skew-Symmetric Matrices
SYM-ILDL is a numerical software package that computes incomplete LDLT (or ‘ILDL’) factorizations of symmetric indefinite and skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally introduced and implemented for symmetric matrices by [Li and Saad, Crout versions of ILU factorization with pivoting for sparse symmetric matrices, Transactions on Nu...
متن کاملSkew-Symmetric Matrix Polynomials and their Smith Forms
Two canonical forms for skew-symmetric matrix polynomials over arbitrary fields are characterized — the Smith form, and its skew-symmetric variant obtained via unimodular congruences. Applications include the analysis of the eigenvalue and elementary divisor structure of products of two skew-symmetric matrices, the derivation of a Smith-McMillan-like canonical form for skew-symmetric rational m...
متن کاملCholesky Factorizations of Matrices Associated with r-Order Recurrent Sequences
In this paper we extend some results on the factorization of matrices associated to Lucas, Pascal, Stirling sequences by the Fibonacci matrix. We provide explicit factorizations of any matrix by the matrix associated with an r-order recurrent sequence Un (having U0 = 0). The Cholesky factorization for the symmetric matrix associated to Un is also obtained.
متن کاملApproximating Matrices with Multiple Symmetries
Abstract. If a tensor with various symmetries is properly unfolded, then the resulting matrix inherits those symmetries. As tensor computations become increasingly important it is imperative that we develop efficient structure preserving methods for matrices with multiple symmetries. In this paper we consider how to exploit and preserve structure in the pivoted Cholesky factorization when appro...
متن کاملThe (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...
متن کامل