Best approximation, tikhonov regularization and reproducing kernelsd

Kodai Mathematical Journal

Volumn 28, Issue 2, 2005, Pages 359-367

  Saitoh, Saburou ^a  

^a GUNMA UNIVERSITY   (Japan)

Author keywords

approximate inverse; Approximation of functions; best approximation; generalized inverse; Moore Penrose generalized inverse; reproducing kernel; Sobolev space; Tikhonov regularization

Indexed keywords

EID: 34547159091     PISSN: 03865991     EISSN: None     Source Type: Journal    
DOI: 10.2996/kmj/1123767016     Document Type: Article

References (7)

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2. C. W. GROETSCH, Inverse Problems in the Mathematical Sciences, Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, 1993.
3. S. SAITOH, Integral Transforms, Reproducing Kernels and their Applications, Pitman Res. Notes in Math. Series 369, Addison Wesley Longman Ltd., UK, 1997.
4. S. SAITOH, Approximate Real Inversion Formulas of the Gaussian Convolution, Applicable Analysis 83 (2004), 727–733.
5. S. SAITOH, T. MATSUURA and M. ASADUZZAMAN, Operator Equations and Best Approximation Problems in Reproducing Kernel Hilbert Spaces, J. of Analysis and Applications 1 (2003), 131–142.
6. S. SAITOH, Constructions by Reproducing Kernels of Approximate Solutions for Linear Differential Equations with L2 Integrable Coefficients, International J. of Math. Sci. 2 (2003), 261–273.
7. T. MATSUURA, S. SAITOH and D. D. TRONG, Approximate and analytical inversion formulas in heat conduction on mutidimensional spaces, J. of Inverse and Ill-posed Problems (to appear).