Multivariate homogeneous two-point Padé approximants and continued fractions

The multivariate homogeneous two-point Padé approximants have been defined and studied recently. In the current work, we consider higher-order approximants and derive error formulas of these approximants using orthogonality conditions. Diverse three-term recurrence relations satisfied by the monic o...

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Vydáno v:Computational & applied mathematics Ročník 39; číslo 1
Hlavní autoři: Chakir, Y., Abouir, J., Benouahmane, B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.03.2020
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Applied physics
Approximants
Computational mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Multivariate analysis
Orthogonality
Pade approximation
Polynomials
Power series
Quotients
41A20
Orthogonal polynomials
41A21
Two-point Padé approximants
65D15
qd-algorithm
Multivariate approximants
Continued fractions
ISSN:2238-3603, 1807-0302
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Shrnutí:The multivariate homogeneous two-point Padé approximants have been defined and studied recently. In the current work, we consider higher-order approximants and derive error formulas of these approximants using orthogonality conditions. Diverse three-term recurrence relations satisfied by the monic orthogonal polynomials are presented. Various continued fractions provided by these relations and the quotient-difference algorithm applied to a power series (positive or negative exponents) are described in terms of their relationships with the multivariate homogeneous two-point Padé table. Numerical examples are furnished to illustrate our results.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-019-0929-y