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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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