Interpolation integral continued fraction with twofold node

Демків, І. І.; Ivasiuk, I.; Kopach, М. І.

doi:10.23939/mmc2019.01.001

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…Theorem 2. In order for there to be an unique rational interpolation functional (3), ( 4), ( 8), (10), (11), on a continual set of nodes (1)…”

Section: Formulation Of the Problem And Solutionmentioning

confidence: 99%

“…Note, that the interpolant (3), ( 4), ( 8), (10), (11) is the one that holds any rational functional of the form (3). 3), ( 4) and (11) we obtain…”

Section: Formulation Of the Problem And Solutionmentioning

confidence: 99%

“…In the papers [3][4][5], the polynomial approximation of functionals is researched. The works [6][7][8][9][10] are devoted to the representation of functionals by chain fractions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Interpolational $(L,M)$-rational integral fraction on a continual set of nodes

Baranetskij

Демків

Kopach

et al. 2021

Carpathian Math. Publ.

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“…Theorem 2. In order for there to be an unique rational interpolation functional (3), ( 4), ( 8), (10), (11), on a continual set of nodes (1)…”

Section: Formulation Of the Problem And Solutionmentioning

confidence: 99%

“…Note, that the interpolant (3), ( 4), ( 8), (10), (11) is the one that holds any rational functional of the form (3). 3), ( 4) and (11) we obtain…”

Section: Formulation Of the Problem And Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Interpolational $(L,M)$-rational integral fraction on a continual set of nodes

Baranetskij

Демків

Kopach

et al. 2021

Carpathian Math. Publ.

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Interpolation rational integral fraction of nth order on a continuum set of nodes

Демків

Baranetskyi

Berehova

2021

Fìz.-mat. model. ìnf. tehnol.

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The paper constructs and investigates an integral rational interpolant of the nth order on a continuum set of nodes, which is the ratio of a functional polynomial of the first degree to a functional polynomial of the (n-1)th degree. Subintegral kernels are determined from the corresponding continuum conditions. Additionally, we obtain an integral equation to determine the kernel of the numerator integral. This integral equation, using elementary transformations, is reduced to the standard form of the integral Volterra equation of the second kind. Substituting the obtained solution into expressions for the rest of the kernels, we obtain expressions for all kernels included in the integral rational interpolant. Then, in order for a rational functional of the nth order to be interpolation on continuous nodes, it is sufficient for this functional to satisfy the substitution rule. Note that the resulting interpolant preserves any rational functional of the obtained form.

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Interpolation rational integral fraction of the Hermitian-type on a continual set of nodes

Baranetskij¹,

Демків²,

Kopach³

et al. 2021

Mat. Stud.

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Some approaches to the construction of interpolation rational integral approximations with arbitrary multiplicity of nodes are analyzed. An integral rational Hermitian-type interpolant of the third order on a continual set of nodes, which is the ratio of a functional polynomial of the first degree to a functional polynomial of the second degree, is constructed and investigated. The resulting interpolant is one that holds any rational functional of the resulting form. Проаналізовано ряд підходів до побудови інтерполяційних раціональних інтегральних наближень з довільною кратністю вузлів. Будується та досліджується інтегральний раціональний інтерполянт типу Ерміта третього порядку на континуальній множині вузлів, який є відношенням функціонального полінома першого степеня до функціонального полінома другого степеня. Одержаний інтерполянт є таким, що зберігає будь який раціональний функціонал одержаного вигляду.

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Interpolation integral continued fraction with twofold node

Cited by 3 publications

References 4 publications

Interpolational $(L,M)$-rational integral fraction on a continual set of nodes

Interpolational $(L,M)$-rational integral fraction on a continual set of nodes

Interpolation rational integral fraction of nth order on a continuum set of nodes

Interpolation rational integral fraction of the Hermitian-type on a continual set of nodes

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