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Published in:
2012 | OriginalPaper | Chapter
Perturbation Bounds for the Nonlinear Matrix Equation
Authors : Ivan Popchev, Petko Petkov, Mihail Konstantinov, Vera Angelova
Published in: Large-Scale Scientific Computing
Publisher: Springer Berlin Heidelberg
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In this paper we make a complete perturbation analysis of the nonlinear matrix equation
, where
A
and
B
are square complex matrices,
denotes the complex conjugate transpose of the matrix
A
and
I
is the identity matrix. We obtain local (first order) perturbation bounds and a non-local perturbation bound for the solution to the equation. The perturbation bounds allow to derive condition and accuracy estimates for the computed solution, when using a stable numerical algorithm to solve the equation.