Nargol Rezvani

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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(More)
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(More)
When working with empirical polynomials, it is important not to introduce unnecessary changes of basis, because that can destabilize fundamental algorithms such as evaluation and rootfinding: for more details, see e.g. [3, 4]. Moreover, in these references it has been shown to be optimal, in a certain sense, to work solely in the Lagrange basis for(More)
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(More)
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