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A Method for Solving Large Matrix Equations Reduced From Fredholm Integral Equations of the Second Kind

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Masahiro HashimotoAuthors Info & Claims

Journal of the ACM (JACM), Volume 17, Issue 4

Pages 629 - 636

https://doi.org/10.1145/321607.321612

Published: 01 October 1970 Publication History

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Abstract

The method of reducing a Fredholm integral equation of the second kind to a matrix equation and then inverting the matrix is well suited to a machine computation. The number of the dimension of the matrix equation is desired to be large for a well approximated solution. However, much computing time may be required to invert the matrix or the number of the elements of the matrix may exceed the memory capacity. A successive iterative method is suggested to avoid these difficulties.

References

[1]

FADDEEVA, V.N. Computational Methods of Linear Algebra. Dover, New York, 1959, p. 62.

Google Scholar

[2]

KANTROVITCH, L. V., AND KRYLOV, V.I. Approximate Methods of Higher Analysis. Noordhoff, Groningen, 1958, pp. 97-161.

Google Scholar

[3]

MIKHLIN, S.G. Linear Integral Equations. Hindustan Pub., Dehli, 1960.

Google Scholar

[4]

POGOROZELSKI, W. IntegralEquations and Their Applications. Pergamon, New York, 1966.

Google Scholar

[5]

VAROA, R.S. Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, N. J., 1962.F

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Cited By

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Dellwo D(1989)Accelerated spectral refinement with applications to integral operatorsSIAM Journal on Numerical Analysis10.1137/072606626:5(1184-1193)Online publication date: 1-Oct-1989
https://dl.acm.org/doi/10.1137/0726066
Dellwo D(1988)Accelerated Refinement with Applications to Integral EquationsSIAM Journal on Numerical Analysis10.1137/072507525:6(1327-1339)Online publication date: 1-Dec-1988
https://dl.acm.org/doi/10.1137/0725075
Amini S(1987)An iterative method for the boundary element solution of the exterior acoustic problemJournal of Computational and Applied Mathematics10.1016/0377-0427(87)90128-220:1(109-117)Online publication date: 1-Nov-1987
https://dl.acm.org/doi/10.1016/0377-0427%2887%2990128-2
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Index Terms

A Method for Solving Large Matrix Equations Reduced From Fredholm Integral Equations of the Second Kind
1. Mathematics of computing
  1. Mathematical analysis
    1. Integral equations
    2. Numerical analysis
      1. Computations on matrices

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Published In

Journal of the ACM Volume 17, Issue 4

Oct. 1970

169 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321607

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1970

Published in JACM Volume 17, Issue 4

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Dellwo D(1989)Accelerated spectral refinement with applications to integral operatorsSIAM Journal on Numerical Analysis10.1137/072606626:5(1184-1193)Online publication date: 1-Oct-1989
https://dl.acm.org/doi/10.1137/0726066
Dellwo D(1988)Accelerated Refinement with Applications to Integral EquationsSIAM Journal on Numerical Analysis10.1137/072507525:6(1327-1339)Online publication date: 1-Dec-1988
https://dl.acm.org/doi/10.1137/0725075
Amini S(1987)An iterative method for the boundary element solution of the exterior acoustic problemJournal of Computational and Applied Mathematics10.1016/0377-0427(87)90128-220:1(109-117)Online publication date: 1-Nov-1987
https://dl.acm.org/doi/10.1016/0377-0427%2887%2990128-2
Faddeev DFaddeeva V(1981)Computational methods of linear algebraJournal of Soviet Mathematics10.1007/BF0108654415:5(531-650)Online publication date: 1981
https://doi.org/10.1007/BF01086544
Duff I(1977)A survey of sparse matrix researchProceedings of the IEEE10.1109/PROC.1977.1051465:4(500-535)Online publication date: 1977
https://doi.org/10.1109/PROC.1977.10514
Atkinson K(1974)Iterative variants of the Nyström method for the numerical solution of integral equationsNumerische Mathematik10.1007/BF0143661822:1(17-31)Online publication date: 1-Feb-1974
https://dl.acm.org/doi/10.1007/BF01436618

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Abstract

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Numerical treatment of boundary value problems by solving a system of second kind Fredholm integral equations

Hybrid function method for solving Fredholm and Volterra integral equations of the second kind

Approximate solutions of Fredholm integral equations of the second kind

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