Singular values of two-parameter matrices: an algorithm to accurately find their intersections

Luca Dieci and Alessandro Pugliese

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 4, 1255-1269

Abstract: Consider the singular value decomposition (SVD) of a two-parameter function A(x), x∈Ω⊂R2, where Ω is simply connected and compact, with boundary Γ. No matter how differentiable the function A is (even analytic), in general the singular values lose all smoothness at points where they coalesce. In this work, we propose and implement algorithms which locate points in Ω where the singular values coalesce. Our algorithms are based on the interplay between coalescing singular values in Ω, and the periodicity of the SVD-factors as one completes a loop along Γ.

Keywords: Two-parameter continuation; Conical intersection; Singular value decomposition; Bisection; Periodicity (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:4:p:1255-1269

DOI: 10.1016/j.matcom.2008.03.012

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