The conjugate gradient method for solving fredholm integral equations of the second kind

References

• Anselone , P. M. 1971 . Collectively Compact Operator Approximation Theory and Applications to Integral Equations , New Jersey : Prentice-Hall Inc. .
   Google Scholar
• Atkinson , K. E. 1975 . Convergent rates for approximate eigenvalues of compact integral operators . SIAM, J. Numer. Anal. , 12 : 213 – 222 .
   Google Scholar
• Atkinson , K. E. 1976 . A survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind , Philadelphia : SIAM .
   Google Scholar
• Axelsson , O. and Lindskog , G. 1986 . On eigenvalue distribution of a class of preconditioning methods . Num. Math. , 48 : 479 – 498 .
   Web of Science ®Google Scholar
• Baker , C. T. H. 1971 . The deferred approach to the limit for eigenvalues of integral equations . SIAM J. Num. Anal. , 8 : 1 – 10 .
   Web of Science ®Google Scholar
• Baker , C. T. H. 1977 . The Numerical Treatment of Integral Equations , Oxford : Clarendon Press .
   Google Scholar
• Chandra R. Conjugate Gradient Method for Partial Differential Equations Dept. Computer Science, Yale Univ. New Haven, CT 1978 Ph.D. Thesis
   Google Scholar
• Dongarra , J. , Bunch , J. , Moler , C. and Stewart , G. 1979 . Unpack User's Guide , Philadelphia : SIAM .
   Google Scholar
• Eisenstat , S. T. , Elman , H. C. and Schultz , M. H. 1983 . Variational iterative methods for nonsymmetric systems of linear equations . SIAM J. Num. Anal. , 20 : 345 – 357 .
   Web of Science ®Google Scholar
• Fenyö , I. and Stolle , H. 1983 . Theorie und Praxis der linearen Integralgleichungen , Basel : Birkhäuser .
   Google Scholar
• Flores J. Iteration Methods for Solving Integral Equations of the Second Kind University of Iowa Iowa, Iowa 1990 Ph.D thesis
   Google Scholar
• Garbow B. Boyle J. Dongarra J. Moler C. Matrix Eigensystem Routines-EISPACK Guide Extension Springer-Verlag 1976 51 Lectures Notes in Computer Science
   Google Scholar
• Golub , G. and Van Loan , C. 1983 . Matrix Computation , Baltimore : Johns Hopkins Press .
   Google Scholar
• Hayes , R. M. 1954 . Iterative methods of solving linear problems on Hilbert space . Nat. Bureau of Standard Appl. math. Ser. , 39 : 71 – 103 .
   Google Scholar
• Hestenes , M. and Stiefel , E. 1952 . Methods of conjugate gradients for solving linear systems . J. Res. Nat. Bur. Stand. , 49 : 409 – 439 .
   Google Scholar
• Hille , E. and Tamarkin , J. D. 1931 . On the characteristic values of linear integral equations . Acta Math. , 57 : 1 – 76 .
   Google Scholar
• Joly , P. 1984 . Méthods de gradient conjugué . Publications du Laboratorie d' Analyse Numérique , 6
   Google Scholar
• Kantorovic , L. V. and Akilov , G. P. 1964 . Functional Analysis in a Normed Space , New York : Pergamon Press .
   Google Scholar
• Smith B. T. Boyle J. Garbow B. Ikebe Y. Klema V. Moler C. Springer-Verlag 1976 6 Matrix eigensystem routines-EISPACK Guide, 2nd ed., Lectures Notes in Computer Science
   Google Scholar
• Swann , D. W. 1971 . Some new classes of kernels whose Fredholm determinants have order less than one . Trans. Amer. Math. Soc. , 160 : 427 – 435 .
   Google Scholar
• Van Der Sluis , A. and Van Der Vorst , H. 1986 . The rate of convergence of conjugate gradients . Numer. Math. , 48 : 543 – 560 .
   Web of Science ®Google Scholar
• Wielandt , H. 1956 . Error bounds for eigenvalues of symmetric integral equations . Proc. AMS Symposium Appl. Math , 6 : 261 – 282 .
   Google Scholar
• Winther , R. 1980 . Some superlinear convergence results for the conjugate gradient method . SIAM J. Numer. Anal. , 17 : 14 – 17 .
   Web of Science ®Google Scholar