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Numerical Functional Analysis and Optimization Volume 12, 1991 - Issue 5-6
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Original Articles

An Application of Approximation Theory to Numerical Solutions for

Hideaki Kaneko Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia, 23529-0077
&
Richard Noren Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia, 23529-0077
Pages 517-523 | Published online: 15 May 2007

References

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  • de Boor , C. 1968 . On uniform approximation by splines . J. of Approx. Thy. , 1 : 219 – 235 .
  • de Boor , C. 1973 . “ Good approximation by splines with variable knots ” . In Spline Functions and Approximation Theory , Basel : Birkhauser Verlag .
  • Graham , I. 1982 . Singularity expansions for the solution of second kind Fredholm integral equations with weakly singular convolution kernals . J. Int. Eq. , 4 : 1 – 30 .
  • Graham , I. and Schneider , C. 1985 . “ Product integration for weakly singular integral equations ” . In Constructive Methods for the Practical Treatment of Integral Equations , Edited by: Hammerlin , G. and Hoffman , K. Vol. 73 , Birkhauser : ISNM .
  • Kaneko , H. and Noren , R. 1990 . An application of approximation theory to the numerical solution of a Fredholm equation with a mild singularity . Appl. Math, and Comp. , 37 : 57 – 66 .
  • Kaneko , H. , Noren , R. and Xu , Y. 1990 . Regularity of the solution of Hammer stein equations with weakly singular kernals . J. Int. Eq. and Op. Th. , 13 : 660 – 670 .
  • Rice , J. R. 1969 . “ On the degree of convergence of nonlinear spline approximation ” . In Approximations with special emphasis on Spline Functions , Edited by: Schoenberg , I. J. 349 – 365 . N.Y. : Academic Press .
  • Richter , G. R. 1976 . On Weakly Singular Fredholm Integral Equations with Displacement Kernels . J. Math. Anal, and Appl. , 55 : 32 – 42 .
  • Schneider , C. 1979 . Regularity of the solution to a class of weakly singular Fredholm integral equations of the second kind . Integral Eqs. and Op. Thy. , 2/1 : 62 – 68 .
  • Shumaker , L. L. 1981 . Wiley-Interscience : Spline Functions-Basic Theory .
  • Vainikko , G. and Pedas , A. 1981 . The properties of Solutions of Weakly Singular Integral Equations . Jl. Austral. Math. Soc. , 22 : 419 – 430 .

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