منابع مشابه
RECSY - A High Performance Library for Sylvester-Type Matrix Equations
RECSY is a library for solving triangular Sylvester-type matrix equations. Its objectives are both speed and reliability. In order to achieve these goals, RECSY is based on novel recursive blocked algorithms, which call high-performance kernels for solving small-sized leaf problems of the recursion tree. In contrast to explicit standard blocking techniques, our recursive approach leads to an au...
متن کاملOn the numerical solution of generalized Sylvester matrix equations
The global FOM and GMRES algorithms are among the effective methods to solve Sylvester matrix equations. In this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two CG-type algorithms for solving generalized Sylvester matrix equations. The proposed methods are iterative projection metho...
متن کاملOn Weakly Formulated Sylvester Equations and Applications
We use a “weakly formulated” Sylvester equation H1/2TM−1/2 −H−1/2TM1/2 = F to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known results of Davis and Kahan. Another application is a bound for the square root of a positive selfadjoint operator which extends the known rule: “The relative error in the squar...
متن کاملOn ADI Method for Sylvester Equations
This paper is concerned with numerical solutions of large scale Sylvester equations AX −XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li andWhite (2002) demonstrated that the so called Cholesky factored ADI method with decent shift parameters can be very effective. In this paper we present a ge...
متن کاملOn the ADI method for Sylvester equations
This paper is concerned with the numerical solution of large scale Sylvester equations AX −XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li and White (2002) demonstrated that the so called Cholesky factor ADI method with decent shift parameters can be very effective. In this paper we present a ...
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ژورنال
عنوان ژورنال: Journal of the Franklin Institute
سال: 2015
ISSN: 0016-0032
DOI: 10.1016/j.jfranklin.2015.03.012