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

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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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Correspondence to Gu Chuan-qing Doctor  (顾传青).

Additional information

Communicated by YE Zhi-ming

Project supported by the National Natural Science Foundation of China (No.10271074)

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Gu, Cq., Pan, Bz. & Wu, Bb. Orthogonal polynomials and determinant formulas of function-valued Padé-type approximation using for solution of integral equations. Appl Math Mech 27, 853–860 (2006). https://doi.org/10.1007/s10483-006-0616-y

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  • DOI: https://doi.org/10.1007/s10483-006-0616-y

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Chinese Library Classification

2000 Mathematics Subject Classification

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