SIAM Journal on Numerical Analysis
Fundamentals of matrix computations
Fundamentals of matrix computations
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Total Least Norm Formulation and Solution for Structured Problems
SIAM Journal on Matrix Analysis and Applications
Structured Total Least Norm for Nonlinear Problems
SIAM Journal on Matrix Analysis and Applications
Computation of approximate polynomial GCDs and an extension
Information and Computation
Polynomials and Linear Control Systems
Polynomials and Linear Control Systems
A composite algorithm for finding zeros of real polynomials
A composite algorithm for finding zeros of real polynomials
Algorithm 835: MultRoot---a Matlab package for computing polynomial roots and multiplicities
ACM Transactions on Mathematical Software (TOMS)
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
The calculation of the degree of an approximate greatest common divisor of two polynomials
Journal of Computational and Applied Mathematics
QR factoring to compute the GCD of univariate approximate polynomials
IEEE Transactions on Signal Processing
The numerical condition of univariate and bivariate degree elevated Bernstein polynomials
Journal of Computational and Applied Mathematics
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This paper considers structured matrix methods for the calculation of the theoretically exact roots of a polynomial whose coefficients are corrupted by noise, and whose exact form contains multiple roots. The addition of noise to the exact coefficients causes the multiple roots of the exact form of the polynomial to break up into simple roots, but the algorithms presented in this paper preserve the multiplicities of the roots. In particular, even though the given polynomial is corrupted by noise, and all computations are performed on these inexact coefficients, the algorithms 'sew' together the simple roots that originate from the same multiple root, thereby preserving the multiplicities of the roots of the theoretically exact form of the polynomial. The algorithms described in this paper do not require that the noise level imposed on the coefficients be known, and all parameters are calculated from the given inexact coefficients. Examples that demonstrate the theory are presented.