Sensitivity Analysis for Computing Orthogonal Polynomials of Sobolev Type

Zhang, Minda

doi:10.1007/978-1-4684-7415-2_38

Cited by 4 publications

(3 citation statements)

References 4 publications

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“…To the best of our knowledge, the computational aspects of Sobolev inner products have not been studied previously up to for the real line case in an unpublished manuscript due to Van Assche [17], and the contributions [7,18]. We follow the same schedule and uses the same ideas given in the manuscript [17].…”

Section: Discrete Sobolev Orthogonal Polynomialsmentioning

confidence: 99%

On computational aspects of discrete Sobolev inner products on the unit circle

Castillo¹,

Garza²,

Marcellán³

2013

Applied Mathematics and Computation

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In this paper, we show how to compute in Oðn 2 Þ steps the Fourier coefficients associated with the Gelfand Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located out side the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product.

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Section: Discrete Sobolev Orthogonal Polynomialsmentioning

confidence: 99%

On computational aspects of discrete Sobolev inner products on the unit circle

Castillo¹,

Garza²,

Marcellán³

2013

Applied Mathematics and Computation

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“…The conditioning of this map has been studied in [28], and an algorithm, analogous to the modified Chebyshev algorithm, developed (for s = 1) in [15]. The corresponding routine in Matlab is [B,normsq]=chebyshev sob(N,mom,abm).…”

Section: Sobolev Orthogonal Polynomialsmentioning

confidence: 99%

Orthogonal polynomials (in Matlab)

Gautschi

2005

Journal of Computational and Applied Mathematics

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A suite of Matlab programs has been developed as part of the book "Orthogonal Polynomials: Computation and Approximation" expected to be published in 2004. The package contains routines for generating orthogonal polynomials as well as routines dealing with applications. In this paper, a brief review is given of the first part of the package, dealing with procedures for generating the three-term recurrence relation for orthogonal polynomials and more general recurrence relations for Sobolev orthogonal polynomials. Moment-based methods and discretization methods, and their implementation in Matlab, are among the principal topics discussed.

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“…It is usually advantageous to choose the family to be a sequence of orthogonal polynomials with respect to an inner product on R, such as a sequence of Chebyshev or Laguerre polynomials; see Beckermann and Bourreau [3], as well as Fischer [5] and Gautschi [7,8,9] for discussions. Related results for Sobolev inner products on a real interval are discussed by Zhang [32]. Gautschi and Zhang [10] describe numerical methods using modified moments in this context.…”

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confidence: 99%

Sensitivity analysis for Szegő polynomials

Kim

Reichel

2009

Numer. Math.

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Abstract. Szegő polynomials are orthogonal with respect to an inner product on the unit circle. Numerical methods for weighted least-squares approximation by trigonometric polynomials conveniently can be derived and expressed with the aid of Szegő polynomials. This paper discusses the conditioning of several mappings involving Szegő polynomials and, thereby, sheds light on the sensitivity of some approximation problems involving trigonometric polynomials.

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Sensitivity Analysis for Computing Orthogonal Polynomials of Sobolev Type

Cited by 4 publications

References 4 publications

On computational aspects of discrete Sobolev inner products on the unit circle

On computational aspects of discrete Sobolev inner products on the unit circle

Orthogonal polynomials (in Matlab)

Sensitivity analysis for Szegő polynomials

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