Iterative solution of a class of linear equations with application to reconstruction of three-dimensional object arrays

An iterative algorithm baaed on probabilistic estimation is described for obtaining the minimum-norm solution of a very large, consistent, linear system of equations AX = g where A is an (m times n) matrix with non-negative elements, x and g are respectively (n times 1) and (m times 1) vectors with positive components.

[1]  Handbook of Numerical Matrix Inversion and Solution of Linear Equations. , 1968 .

[2]  J. Westlake Handbook of Numerical Matrix Inversion and Solution of Linear Equations , 1968 .

[3]  G. Herman,et al.  Three-dimensional reconstruction from projections: a review of algorithms. , 1974, International review of cytology.

[4]  G. Stewart,et al.  On the Numerical Properties of an Iterative Method for Computing the Moore–Penrose Generalized Inverse , 1974 .

[5]  G T Herman,et al.  ART: mathematics and applications. A report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques. , 1973, Journal of theoretical biology.

[6]  Azriel Rosenfeld,et al.  FUZZY GRAPHS††The support of the Office of Computing Activities, National Science Foundation, under Grant GJ-32258X, is gratefully acknowledged, as is the help of Shelly Rowe in preparing this paper. , 1975 .

[7]  D. Luenberger Optimization by Vector Space Methods , 1968 .

[8]  Robert Todd Gregory,et al.  A collection of matrices for testing computational algorithms , 1969 .

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

[10]  S. S. Prabhu,et al.  Reconstruction of objects from their projections using generalized inverses , 1974, Comput. Graph. Image Process..

[11]  S. S. Prabhu,et al.  Probabilistic reinforcement algorithms for the reconstruction of pictures from their projections , 1973 .

[12]  Nasser E. Nahi,et al.  Estimation Theory and Applications , 1969 .

[13]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .