Consider the singular value decomposition (SVD) of a two-parameter function A(x), x@?@W@?R^2, where @W is simply connected and compact, with boundary @C. 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 @W where the singular values coalesce. Our algorithms are based on the interplay between coalescing singular values in @W, and the periodicity of the SVD-factors as one completes a loop along @C.
['Luca Dieci', 'Alessandro Pugliese']
Singular values of two-parameter matrices: an algorithm to accurately find their intersections