Function-valued Padé-type approximant via E-algorithm and its applications in solving integral equations

The function-valued Padé-type approximant ( FPTA) was defined in the inner product space [8]. In this work, we choose the coefficients in the Neumann power series to make the inner product with both sides a function-valued system of equations to yield a scalar system. Then we express an FPTA in the...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 217; no. 20; pp. 7975 - 7984
Main Authors: Gu, Chuanqing, Tao, Youtian
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.06.2011
Elsevier
Subjects:
Approximants
Characteristic function
Characteristic value
Computation
Determinants
Exact sciences and technology
Fredholm integral equation
Function-valued padé approximant
Functional analysis
Integral equations
Mathematical analysis
Mathematical models
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Power series
Recursive algorithm
Scalars
Sciences and techniques of general use
Characteristic function
Function-valued padé approximant
Fredholm integral equation
Recursive algorithm
Characteristic value
Transcendental equation
Numerical integration
Numerical linear algebra
Determinant
Power series
Fredholm equation
Equation system
Numerical approximation
Non linear equation
Numerical analysis
Applied mathematics
Algebraic equation
Integral equation
Padé approximant
Inner product space
ISSN:0096-3003, 1873-5649
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Summary:The function-valued Padé-type approximant ( FPTA) was defined in the inner product space [8]. In this work, we choose the coefficients in the Neumann power series to make the inner product with both sides a function-valued system of equations to yield a scalar system. Then we express an FPTA in the determinant form. To avoid the direct computation of the determinants, we present the E-algorithm for FPTA based on the vector-valued E-algorithm given by Brezinski [4]. The method of FPTA via E-algorithm ( FPTAVEA) not only includes all previous methods but overcomes their essential difficulties. The numerical experiment for a typical integral equation [1] illustrates that the method of FPTAVEA is simpler and more effective for obtaining the characteristic values and the characteristic functions than all previous methods. In addition, this method is also applicable to other Fredholm integral equations of the second kind without explicit characteristic values and characteristic functions. A corresponding example [12] is given and the numerical result is the same as that in [12].
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.02.090