[1] Hào D N, Hien P M. Stability results for the cauchy problem for the laplace equation in a strip. Inverse Problems, 2003, 19(4):833-844
[2] Li Z, Fu C L. A mollification method for a cauchy problem for the laplace equation. Applied Mathematics and Computation, 2011, 217(22):9209-9218
[3] Vani C, Avudainayagam A. Regularized solution of the Cauchy problem for the Laplace equation using Meyer wavelets. Mathematical and Computer Modelling, 2002, 36(9-10):1151-1159
[4] Qiu C Y, Fu C L. Wavelets and regularization of the Cauchy problem for the Laplace equation. Journal of Mathematical Analysis and Applications, 2008, 338(2):1440-1447
[5] Fu C L, Li H F, Qian Z, Xiong X T. Fourier regularization method for solving a Cauchy problem for the Laplace equation. Inverse Problems in Science and Engineering, 200816(2):159-169
[6] Gorenflo R. Funktionentheoretische bestimmung des aussenfeldes zu einer zweidimensionalen magnetohydrostatischen konfiguration. Zeitschrift Angewandte Mathematik und Physik, 1965, 16:279-290
[7] Franzone P C, Magenes E. On the inverse potential problem of electrocardiology. Calcolo, 1979, 16(4):459-538
[8] Johnson C R. Computational and numerical methods for bioelectric field problems. Critical Reviews in Biomedical Engineering, 1997, 25(1):1-81
[9] Alessandrini G. Stable determination of a crack from boundary measurements. Proc R Soc Edinb Sect A, 1993, 123:497-516
[10] Deng Z L, Fu C L, Feng X L, Zhang Y X. A mollification regularization method for stable analytic continuation. Mathematics and Computers in Simulation, 2011, 81(8):1593-1608
[11] Klann E, Ramlau R, Reichel L. Wavelet-based multilevel methods for linear ill-posed problems. BIT Numerical Mathematics, 2011, 51(3):669-694
[12] Cao H, Pereverzev S V. The balancing principle for the regularization of elliptic cauchy problems. Inverse Problems, 2007, 23(5):1943-1956
[13] Cao H, Klibanov M V, Pereverzev S V. A carleman estimate and the balancing principle in the quasireversibility method for solving the cauchy problem for the laplace equation. Inverse Problems, 2009, 25(3):035005
[14] Zhao Z Y, Liu J F. Hermite spectral and pseudospectral methods for numerical differentiation. Applied Numerical Mathematics, 2011, 61(12):1322-1330
[15] Zhao Z Y. Numerical analytic continuation by a mollification method based on hermite function expansion. Inverse Problems, 2012, 28(4):045002
[16] Szegö S. Orthogonal Polynomials. Providence, RI:Amer Mathematical Society, 1975
[17] Hille E. Contributions to the theory of Hermitian series Ⅱ. The representation problem. Transactions of the American Mathematical Society, 1940, 47(1):80-94
[18] Tautenhahn U. Optimality for ill-posed problems under general source conditions. Numerical Functional Analysis and Optimization, 1998, 19(3):377-398
[19] Fu C L, Dou F F, Feng X L, Qian Z. A simple regularization method for stable analytic continuation. Inverse Problems, 2008, 24:065003 |