Introduction to functional analysis, 2nd ed.
Introduction to functional analysis, 2nd ed.
Computing the Extremal Positive Definite Solutions of a Matrix Equation
SIAM Journal on Scientific Computing
On the Solution of a Nonlinear Matrix Equation arising in Queueing Problems
SIAM Journal on Matrix Analysis and Applications
Iterative solution of two matrix equations
Mathematics of Computation
Polynomials and Linear Control Systems
Polynomials and Linear Control Systems
A Shifted Cyclic Reduction Algorithm for Quasi-Birth-Death Problems
SIAM Journal on Matrix Analysis and Applications
Structured Markov chains solver: algorithms
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Structured Markov chains solver: tool extension
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
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We show that some classes of matrix equations can be reduced to solving a quadratic matrix equation of the kind X2A + XB + C = 0 where A,B,C,X are m × m matrices or semi-infinite matrices. The problem of computing the minimal solution, if it exists, of the latter equation is reduced to computing the matrix coefficients Ho and H-1 of the Laurent matrix series H(z) = Σi=-∞+∞ ziHi such that H(z)(zA+B+z-1C) = I. Known algorithms for this computation are revisited in terms of operations among block Toeplitz matrices and new algorithms are introduced. An application to the solution of Non-Skip-Free Markov chains is shown.