Computing the nearest singular univariate polynomials with given root multiplicities. (English) Zbl 1291.65082
Summary: We derive explicit expressions for the nearest singular polynomials with given root multiplicities and its distance to the given polynomial. These expressions can be computed recursively. These results extend previous results [L. Zhi et al., Japan J. Ind. Appl. Math. 21, No. 2, 149–162 (2004; Zbl 1138.65049); L. Zhi and W. Wu, J. Symb. Comput. 26, No. 6, 667–675 (1998; Zbl 0917.65055)].
MSC:
65D99 | Numerical approximation and computational geometry (primarily algorithms) |
68W30 | Symbolic computation and algebraic computation |
12D10 | Polynomials in real and complex fields: location of zeros (algebraic theorems) |
26C10 | Real polynomials: location of zeros |
41A10 | Approximation by polynomials |
Software:
MultRootReferences:
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