Teresa Regińska

My research interest concerns numerical analysis in abstract spaces, spectral approximation, eigenvalue localization and ill posed problems regularization. Recently I am working on application of wavelets to construction of regularized solutions of ill posed problems.

Selected Publications:

• Sideways heat equation and wavelets, Journal of Computational and Applied Mathematics, vol.63 pp. 209-214 (1995)
• A regularization parameter in discrete ill--posed problems, SIAM J. Sci. Comput. vol.17, No.3, pp. 740- 749 (1996)
• (with L. Eldén) Numerical solution of the sideways heat equation by a wavelet - Galerkin method, Inverse Problems 13, pp.1093-1106 (1997)
• (with L. Eldén and F Berntsson) Wavelet and Fourier methods for solving the sideways heat equation, SIAM J. Sci. Comput. Vol 21, No.6, pp. 2187-2205, (2000)
• (with L. Eldén) Stability and convergence of wavelet-Galerkin method for sideways heat equation, J. Inverse and Ill-Posed Problems, vol. 8, no.1, pp. 31-49 (2000)
• Application of wavelet shrinkage to solving sideways heat equation, BIT vol.41, no 5, pp. 1101-1110 (2001)
• Regularization parameters choosing for discrete ill-posed problems, in "Inverse Problems in Engineering Mechanics IV" (Proceedings of the International Symposium on ISIP2003) M.Tanaka (ed.), Elsevier 2003, pp. 457-464.
• Regularization of discrete ill-posed problems, BIT Numerical Mathematics vol.44, pp. 119-133 (2004)
• (with A. Wakulicz) Wavelet moment method for Cauchy problem for the Helmholtz equation Preprint IMPAN 662, December 2005) (pdf file)
• (with K. Regiński) Approximate solution of a Cauchy problem for the Helmholtz equation, Inverse Problems 22, pp. 975-989(2006), Preprint IMPAN 660 (pdf file)
• (with K. Regiński) A Cauchy problem for the Helmholtz equation: application to analysis of light propagation in solids, Preprint: Berichtsreihe des Mathematischen Seminars, Christian-Albrechts-Universität zu Kiel, 06-4 (2006)