Padé-Type Approximation and General Orthogonal Polynomials

Brezinski, Claude

doi:10.1007/978-3-0348-6558-6

Cited by 420 publications

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“…The polynomials can be derived by the Gram-Schmidt orthonormalization procedure or by solving the Hankel system based on the moments of the density f 0H (Brezinski 1980). This latter is the approach followed in this study.…”

Section: Theoremmentioning

confidence: 99%

The Henderson Smoother in Reproducing Kernel Hilbert Space

Dagum

Bianconcini

2008

Journal of Business & Economic Statistics

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Section: Theoremmentioning

confidence: 99%

The Henderson Smoother in Reproducing Kernel Hilbert Space

Dagum

Bianconcini

2008

Journal of Business & Economic Statistics

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“…3 Knowing c, the problem is still to approximate h. The original approach [9,8] is to construct an autoregressive (AR) approximant, i.e., one of the form R m (z) = Kz m /Ṽ m (z) with K a constant and V m the orthogonal polynomial with respect to c. A relation similar to (4) can be derived, not for the transfer function h but for "half the Fourier series" Ω(z) = c 0 + 2 k>0 c k z k .…”

Section: Orthogonal Rational Functions Analytic Outside the Unit Diskmentioning

confidence: 99%

Orthogonality Measures and Applications in Systems Theory in One and More Variables

Bultheel

Cuyt

Verdonk

2008

Large-Scale Scientific Computing

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Abstract. The representation or order reduction of a rational transfer function by a linear combination of orthogonal rational functions offers several advantages, among which the possibility to work with prescribed poles and hence the guarantee of system stability. Also for multidimensional linear shift-invariant systems with infinite-extent impulse response, stability can be guaranteed a priori by the use of a multivariate Padé-type approximation technique, which is again a rational approximation technique. In both the one-and multidimensional case the choice of the moment functional with respect to which the orthogonality of the functions in use is imposed, plays a crucial role.

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“…Brezinski and many authors [5] introduced and improved scalar Padé-type approximation. The scalar Padé-type approximants are closely connected to general orthogonal polynomials.…”

Section: Definition and Constructionmentioning

confidence: 99%

Orthogonal polynomials and determinant formulas of function-valued Padé-type approximation using for solution of integral equations

Bao-zhen

2006

Appl Math Mech

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Abstract:To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.

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Padé-Type Approximation and General Orthogonal Polynomials

Cited by 420 publications

References 0 publications

The Henderson Smoother in Reproducing Kernel Hilbert Space

The Henderson Smoother in Reproducing Kernel Hilbert Space

Orthogonality Measures and Applications in Systems Theory in One and More Variables

Orthogonal polynomials and determinant formulas of function-valued Padé-type approximation using for solution of integral equations

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