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Locating coalescing singular values of large two-parameter matrices. (English) Zbl 1210.65089
Summary: Consider a matrix valued function \(A(x)\in \mathbb R^{m \times n}, m \geq n\), smoothly depending on parameters \(x \in \Omega \subset \mathbb R^2\), where \(\Omega\) is simply connected and bounded. We consider a technique to locate parameter values where some of the \(q\) dominant (\(q\leq n\)) singular values of \(A\) coalesce, in the specific case when \(A\) is large and \(m > n \gg q\).

MSC:
65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A18 Eigenvalues, singular values, and eigenvectors
15A23 Factorization of matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F99 Numerical linear algebra
65P30 Numerical bifurcation problems
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