Nargol Rezvani | University of Toronto (original) (raw)
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Graduate Center of the City University of New York
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Papers by Nargol Rezvani
ACM SIGSAM Bulletin, 2005
In his 1999 SIGSAM BULLETIN paper [7], H. J. Stetter gave an explicit formula for finding the nea... more In his 1999 SIGSAM BULLETIN paper [7], H. J. Stetter gave an explicit formula for finding the nearest polynomial with a given zero. This present paper revisits the issue, correcting a minor omission from Stetter's formula and explicitly extending the results to different polynomial bases.Experiments with our implementation demonstrate that the formula may not after all, fully solve the problem,
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - SNC '11, 2011
ABSTRACT This paper extends earlier results on finding nearest polynomials, expressed in various ... more ABSTRACT This paper extends earlier results on finding nearest polynomials, expressed in various polynomial bases, satisfying linear constraints. Results are extended to different bases, including Hermite interpolational bases (not to be confused with the Hermite orthogonal polynomials). Results are also extended to the case of weighted norms, which turns out to be slightly nontrivial, and interesting in practice.
Mathematics in Computer Science, 2007
ABSTRACT . Spectra and pseudospectra of matrix polynomials are of interest in geometric intersect... more ABSTRACT . Spectra and pseudospectra of matrix polynomials are of interest in geometric intersection problems, vibration problems, and analysis of dynamical systems. In this note we consider the effect of the choice of polynomial basis on the pseudospectrum and on the conditioning of the spectrum of regular matrix polynomials. In particular, we consider the direct use of the Lagrange basis on distinct interpolation nodes, and give a geometric characterization of “good” nodes. We also give some tools for computation of roots at infinity via a new, natural, reversal. The principal achievement of the paper is to connect pseudospectra to the well-established theory of Lebesgue functions and Lebesgue constants, by separating the influence of the scalar basis from the natural scale of the matrix polynomial, which allows many results from interpolation theory to be applied.
ACM SIGSAM Bulletin, 2005
In his 1999 SIGSAM BULLETIN paper [7], H. J. Stetter gave an explicit formula for finding the nea... more In his 1999 SIGSAM BULLETIN paper [7], H. J. Stetter gave an explicit formula for finding the nearest polynomial with a given zero. This present paper revisits the issue, correcting a minor omission from Stetter's formula and explicitly extending the results to different polynomial bases.Experiments with our implementation demonstrate that the formula may not after all, fully solve the problem,
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - SNC '11, 2011
ABSTRACT This paper extends earlier results on finding nearest polynomials, expressed in various ... more ABSTRACT This paper extends earlier results on finding nearest polynomials, expressed in various polynomial bases, satisfying linear constraints. Results are extended to different bases, including Hermite interpolational bases (not to be confused with the Hermite orthogonal polynomials). Results are also extended to the case of weighted norms, which turns out to be slightly nontrivial, and interesting in practice.
Mathematics in Computer Science, 2007
ABSTRACT . Spectra and pseudospectra of matrix polynomials are of interest in geometric intersect... more ABSTRACT . Spectra and pseudospectra of matrix polynomials are of interest in geometric intersection problems, vibration problems, and analysis of dynamical systems. In this note we consider the effect of the choice of polynomial basis on the pseudospectrum and on the conditioning of the spectrum of regular matrix polynomials. In particular, we consider the direct use of the Lagrange basis on distinct interpolation nodes, and give a geometric characterization of “good” nodes. We also give some tools for computation of roots at infinity via a new, natural, reversal. The principal achievement of the paper is to connect pseudospectra to the well-established theory of Lebesgue functions and Lebesgue constants, by separating the influence of the scalar basis from the natural scale of the matrix polynomial, which allows many results from interpolation theory to be applied.