Matrix Structures of Vandermonde and Cauchy Types and Polynomial and Rational Computations

Victor Y. Pan
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Victor Y. Pan: Lehman College, CUNY, Department of Mathematics and Computer Science

Chapter Chapter 3 in Structured Matrices and Polynomials, 2001, pp 73-116 from Springer

Abstract: Abstract In this chapter, we complement our subjects of the previous chapter by studying fundamental polynomial and rational computations (this includes the Nevanlinna-Pick and Nehari problems of rational interpolation and approximation as well as sparse multivariate polynomial interpolation) together with the related computations with matrices of Vandermonde and Cauchy types. We also show applications to loss-resilient encoding/decoding and to diagonalization of matrix algebras, which leads us to the discrete sine and cosine transforms. Figures 3.3– 3.6 summarize correlation among computational problems in these areas.

Keywords: Polynomial Interpolation; Hankel Matrix; Vandermonde Matrix; Rational Interpolation; Hessenberg Matrix (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0129-8_3

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DOI: 10.1007/978-1-4612-0129-8_3

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