Error estimates for linear systems with applications to regularization

Numerical Algorithms

Volumn 49, Issue 1-4, 2008, Pages 85-104

  Brezinski, C ^a   Rodriguez, G ^b   Seatzu, S ^b  

^a UNIVERSITÉ LILLE 1   (France)

^b UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

Error estimates; Ill conditioned linear systems; Regularization

Indexed keywords

EID: 55349117124     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-008-9163-1     Document Type: Article

References (17)

1. G. Auchmuty 1992 A posteriori error estimates for linear equations Numer. Math. 61 1 6
2. C. Brezinski 1999 Error estimates for the solution of linear systems SIAM J. Sci. Comput 21 764 781
3. C. Brezinski M. Redivo-Zaglia G. Rodriguez S. Seatzu 1998 Extrapolation techniques for ill-conditioned linear systems Numer. Math. 81 1 29
4. C. Brezinski M. Redivo-Zaglia G. Rodriguez S. Seatzu 2003 Multi-parameter regularization techniques for ill-conditioned linear systems Numer. Math. 94 203 228
5. P. Craven G. Wahba 1979 Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross validation Numer. Math. 31 377 403
6. A. Galantai 2001 A study of Auchmuty's error estimate Comput. Math. Appl. 42 1093 1102
7. G.H. Golub M. Heath G. Wahba 1979 Generalized cross-validation as a method for choosing a good ridge parameter Technometrics 21 2 215 223
8. G.H. Golub U. von Matt 1997 Generalized cross-validation for large-scale problems J. Comput. Graph. Stat 6 1 1 34
9. Golub, G.H., Meurant, G.: Matrices, Moments and Quadrature with Applications. Princeton University Press, Princeton (to appear)
10. P.C. Hansen 1994 Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems Numer. Algorithms 6 1 35
11. Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM, Philadelphia (1998)
12. P.C. Hansen T.K. Jensen G. Rodriguez 2006 An adaptive pruning algorithm for the discrete L-curve criterion J. Comput. Appl. Math. 198 483 492
13. P.C. Hansen D O'Leary 1993 The use of the L-curve in the regularization of discrete ill-posed problems SIAM J. Sci. Statist. Comput. 14 1487 1503
14. Matlab ver. 7.4, The MathWorks, Inc., Natick, MA (2007)
15. C.V.M. van der Mee S. Seatzu 2005 A method for generating infinite positive self-adjoint test matrices and Riesz bases SIAM J. Matrix Anal. Appl. 26 1132 1149
16. Redivo-Zaglia, M., Rodriguez, G.: smt: a Matlab structured matrices toolbox (2007) (in preparation)
17. J.M. Varah 1993 The prolate matrix Linear Algebra Appl. 187 269 278