메뉴 건너뛰기




Volumn 34, Issue 4, 1997, Pages 1357-1390

A kernel-based method for the approximate solution of backward parabolic problems

Author keywords

Ill posed problems; Numerical methods; Parabolic equations; Regularization

Indexed keywords


EID: 0007366017     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994276785     Document Type: Article
Times cited : (68)

References (25)
  • 3
    • 0000425575 scopus 로고
    • Some convergence estimates for semidiscrete Galerkin approximations for parabolic equations
    • J. BRAMBLE, A. SCHATZ, V. THOMEE, AND L. WAHLBIN, Some convergence estimates for semidiscrete Galerkin approximations for parabolic equations, SIAM J. Numer. Anal., 14 (1977), pp. 218-241.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 218-241
    • Bramble, J.1    Schatz, A.2    Thomee, V.3    Wahlbin, L.4
  • 4
    • 84966215657 scopus 로고
    • On the numerical computation of parabolic problems for preceding times
    • B. BUZBEE AND A. CARASSO, On the numerical computation of parabolic problems for preceding times, Math. Comp., 27 (1973), pp. 237-266.
    • (1973) Math. Comp. , vol.27 , pp. 237-266
    • Buzbee, B.1    Carasso, A.2
  • 5
    • 0003116401 scopus 로고
    • Some numerical results for the solution of the heat equation backwards in time
    • John Wiley, New York
    • J. R. CANNON, Some numerical results for the solution of the heat equation backwards in time, in Numerical Solutions of Nonlinear Differential Equations, John Wiley, New York, 1966.
    • (1966) Numerical Solutions of Nonlinear Differential Equations
    • Cannon, J.R.1
  • 6
    • 0007447039 scopus 로고
    • Quasireversibility type methods for non-well posed problems
    • G. CLARK AND S. OPPENHEIMER, Quasireversibility type methods for non-well posed problems, Elect. J. Diff. Eq., (1994); also available online from http://ejde.math.swt.edu/toc.html 1994.
    • (1994) Elect. J. Diff. Eq.
    • Clark, G.1    Oppenheimer, S.2
  • 7
    • 85033129713 scopus 로고    scopus 로고
    • 1994
    • G. CLARK AND S. OPPENHEIMER, Quasireversibility type methods for non-well posed problems, Elect. J. Diff. Eq., (1994); also available online from http://ejde.math.swt.edu/toc.html 1994.
  • 8
    • 0141827559 scopus 로고
    • The construction of solutions of the heat equation backward in time
    • D. COLTON AND J. WIMP, The construction of solutions of the heat equation backward in time, Math. Methods Appl. Sci., 1 (1979), pp. 32-39.
    • (1979) Math. Methods Appl. Sci. , vol.1 , pp. 32-39
    • Colton, D.1    Wimp, J.2
  • 9
    • 0007415654 scopus 로고
    • The approximation of certain parabolic equations backward in time by Sobolev equations
    • R. EWING, The approximation of certain parabolic equations backward in time by Sobolev equations, SIAM J. Math. Anal., 6 (1975), pp. 283-294.
    • (1975) SIAM J. Math. Anal. , vol.6 , pp. 283-294
    • Ewing, R.1
  • 10
    • 0004236492 scopus 로고
    • Johns Hopkins University Press, Baltimore, MD
    • G. GOLUB AND C. VAN LOAN, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1983.
    • (1983) Matrix Computations
    • Golub, G.1    Van Loan, C.2
  • 12
    • 0001273835 scopus 로고
    • Regularization methods for large-scale problems
    • M. HANKE AND P. C. HANSEN, Regularization methods for large-scale problems, Surveys Math. Indust., 3 (1993), pp. 252-315.
    • (1993) Surveys Math. Indust. , vol.3 , pp. 252-315
    • Hanke, M.1    Hansen, P.C.2
  • 13
    • 0141827558 scopus 로고
    • Numerical solution of the heat equation for preceding times
    • P. JOHN, Numerical solution of the heat equation for preceding times, Ann. Mat. Pura Appl., 40 (1955), pp. 129-142.
    • (1955) Ann. Mat. Pura Appl. , vol.40 , pp. 129-142
    • John, P.1
  • 14
    • 58149365283 scopus 로고
    • Future-sequential regularization methods of ill-posed Volterra equations
    • P. K. LAMM, Future-sequential regularization methods of ill-posed Volterra equations, J. Math. Anal. Appl., 195 (1995), pp. 469-494.
    • (1995) J. Math. Anal. Appl. , vol.195 , pp. 469-494
    • Lamm, P.K.1
  • 15
    • 85033157805 scopus 로고    scopus 로고
    • Regularized inversion of finitely smoothing Volterra operators
    • to appear
    • P. K. LAMM, Regularized inversion of finitely smoothing Volterra operators, Inverse Problems, to appear.
    • Inverse Problems
    • Lamm, P.K.1
  • 17
    • 0040132034 scopus 로고
    • Convergence of the conjugate gradient method for compact operators
    • Engl and Groetsch, eds., Academic Press, New York
    • A. LOUIS, Convergence of the conjugate gradient method for compact operators, in Inverse and ill-posed problems, Engl and Groetsch, eds., Academic Press, New York, 1987.
    • (1987) Inverse and Ill-posed Problems
    • Louis, A.1
  • 18
    • 0040225041 scopus 로고
    • Stabilized quasi-reversibility and other nearly-best-possible methods for non-well-posed problems
    • Heriot-Watt University
    • K. MILLER, Stabilized quasi-reversibility and other nearly-best-possible methods for non-well-posed problems, in Symposium on Logarithmic Convexity and Non-Well Posed Problems, Springer Lecture Notes #316, Heriot-Watt University, 1973, pp. 161-176.
    • (1973) Symposium on Logarithmic Convexity and Non-Well Posed Problems, Springer Lecture Notes #316 , vol.316 , pp. 161-176
    • Miller, K.1
  • 19
    • 84968490731 scopus 로고
    • A well-posed problem for the backward heat equation
    • W. L. MIRANKER, A well-posed problem for the backward heat equation, Proc. Amer. Math. Soc., 12 (1961), pp. 243-247.
    • (1961) Proc. Amer. Math. Soc. , vol.12 , pp. 243-247
    • Miranker, W.L.1
  • 22
    • 0039633096 scopus 로고
    • The final value problem for evolution equations
    • R. SHOWALTER, The final value problem for evolution equations, J. Math. Anal. Appl., 47 (1974), pp. 563-572.
    • (1974) J. Math. Anal. Appl. , vol.47 , pp. 563-572
    • Showalter, R.1
  • 25
    • 0002860143 scopus 로고
    • Some superlinear convergence results for the conjugate gradient method
    • R. WINTHER, Some superlinear convergence results for the conjugate gradient method, SIAM J. Numer. Anal., 17 (1980), pp. 14-17.
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 14-17
    • Winther, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.