A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations

BIT

Volumn 28, Issue 3, 1988, Pages 659-670

  Björck, Åke ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

AMS Subject Classification: 65F20; ill posed problems; Lanczos algorithm; regularization

Indexed keywords

EID: 0001644662     PISSN: 00063835     EISSN: 15729125     Source Type: Journal    
DOI: 10.1007/BF01941141     Document Type: Article

References (19)

1. The singular value decomposition in product form
2. Algorithms for the regularization of ill-conditioned least squares problems
3. Generalized cross-validation as a method for choosing a good ridge parameter
4. Calculating the singular values and pseudoinverse of a matrix
5. A block Lanczos method to compute the singular values and the corresponding singular rectors of a matrix
6. Error analysis of the Lanczos algorithm for tri-diagonalizing a symmetric matrix
7. LSQR: an algorithm for sparse linear equations and sparse least squares problems
8. A new look at the Lanczos algorithm for solving symmetric systems of linear equations
9. The Lanczos algorithm with selective orthogonalization
10. The block conjugate gradient algorithm and related methods
11. A bidiagonalization-regularization procedure for large scale discretizations of ill-posed problems
12. Research, development and LINPACK
13. A practical examination of some numerical methods for linear discrete ill-posed problems
14. Some superlinear convergence results for the conjugate gradient method
15. The collinearity problem in linear and non-linear regression. The partial least squares (PLS) approach to generalized inverses