The componentwise distance to the nearest singular matrix
SIAM Journal on Matrix Analysis and Applications
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Structured singular values and stability analysis of uncertain polynomials, part 2: a missing link
Systems & Control Letters
Approximate polynomial greatest common divisors and nearest singular polynomials
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Matrix computations (3rd ed.)
Efficient algorithms for computing the nearest polynomial with constrained roots
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On approximate GCDs of univariate polynomials
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Efficient algorithms for computing the nearest polynomial with a real root and related problems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Structured Perturbations Part I: Normwise Distances
SIAM Journal on Matrix Analysis and Applications
Structured Perturbations Part II: Componentwise Distances
SIAM Journal on Matrix Analysis and Applications
ACM Communications in Computer Algebra
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We explore the problem of computing a nearest singular matrix to a given regular Hankel matrix while preserving the structure of the matrix. Nearness is measured in a matrix norm, or a componentwise norm. A recent result for structured condition numbers leads to an efficient algorithm in the spectral norm. We devise a parametrization of singular Hankel matrices, to discuss other norms.