Dynamical methods for polar decomposition and inversion of matrices
نویسندگان
چکیده
منابع مشابه
Dynamical Methods for Polar Decomposition and Inversion of Matrices
We show how one may obtain polar decomposition as well as inversion of xed and time-varying matrices using a class of nonlinear continuous-time dynamical systems. First we construct a dynamic system that causes an initial approximation of the inverse of a time-varying matrix to ow exponentially toward the true time-varying inverse. Using a time-parameterized homotopy from the identity matrix to...
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Let L(λ) = Inλ m + Am−1λm−1 + · · ·+ A1λ + A0 be an n× n monic matrix polynomial, and let CL be the corresponding block companion matrix. In this note, we extend a known result on scalar polynomials to obtain a formula for the polar decomposition of CL when the matrices A0 and Pm−1 j=1 AjA ∗ j are nonsingular.
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Usznq the recently zntroduced concept of a "dynamzc znverse" of a map, along wzth zts assoczated analog compvtatzonal pnradzgm. we construct contznuous-tame iionlzneor dynamzcal systems whzch produce both regulor and generalazed znverses of ttme-varyzng and $xed matrzccs, as well as polar decomposataons.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(96)00235-2