Generalized Moment Representations and Multivariate Multipoint Padé Approximants

Holub, A. P.; Pozharskiy, O. A.; Chernets’ka, L. O.

doi:10.1007/s11253-020-01729-6

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2021

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“…Representation of functions of several variables by means of branched continued fractions has been an interesting matter of study during the 70 years and has given rise to other important related topics like multivariate Padé approximants, systems of linear algebraic equations, quadratic form, system of partial differential equations and so on (see, e.g., [1,13,14,25,30,39]).…”

Section: Introductionmentioning

confidence: 99%

Approximation of functions of several variables by multidimensional $S$-fractions with independent variables

Dmytryshyn

Sharyn

2021

Carpathian Math. Publ.

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The paper deals with the problem of approximation of functions of several variables by branched continued fractions. We study the correspondence between formal multiple power series and the so-called "multidimensional $S$-fraction with independent variables". As a result, the necessary and sufficient conditions for the expansion of the formal multiple power series into the corresponding multidimensional $S$-fraction with independent variables have been established. Several numerical experiments show the efficiency, power and feasibility of using the branched continued fractions in order to numerically approximate certain functions of several variables from their formal multiple power series.

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Section: Introductionmentioning

confidence: 99%