论文信息 - Characterization of the solutions set of inconsistent least-squares problems by an extended Kaczmarz algorithm

Characterization of the solutions set of inconsistent least-squares problems by an extended Kaczmarz algorithm

We give a new characterization of the solutions set of the general (inconsistent) linear least-squares problem using the set of limit-points of an extended version of the classical Kaczmarz’s projections method. We also obtain a “ step error reduction formula” which, in some cases, can give us apriori information about the convergence properties of the algorithm. Some numerical experiments with our algorithm and comparisons between it and others existent in the literature, are made in the last section of the paper.

C. Popa

[1] L. D. Pyle. A generalized inverse ∈-algorithm for constructing intersection projection matrices, with applications , 1967 .

[2] K. Tanabe. Projection method for solving a singular system of linear equations and its applications , 1971 .

[3] S. R. Searle. Generalized Inverse Matrices , 1971 .

[4] Louis A. Hageman,et al. Iterative Solution of Large Linear Systems. , 1971 .

[5] Masaaki Sibuya,et al. Numerical algorithms for the Moore-Penrose inverse of a matrix: Direct methods , 1972 .

[6] K. S. Banerjee. Generalized Inverse of Matrices and Its Applications , 1973 .

[7] K. Tanabe,et al. Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix , 1977 .

[8] Å. Björck,et al. Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations , 1979 .

[9] Gene H. Golub,et al. Matrix computations , 1983 .

[10] An iterative method for CVBEM systems Part I: The Kaczmarz algorithm , 1993 .

[11] Constantin Popa,et al. Least-squares solution of overdetermined inconsistent linear systems using kaczmarz's relaxation , 1995, Int. J. Comput. Math..