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RISS 인기검색어
- 검색키워드
- 저자 : Shwetabh Srivastava (검색결과 4 건)
- 무료
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AN ITERATIVE METHOD FOR ORTHOGONAL PROJECTIONS OF GENERALIZED INVERSES
Srivastava, Shwetabh,Gupta, D.K. The Korean Society for Computational and Applied M 2014 Journal of applied mathematics & informatics Vol.32 No.1
This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.
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Higher order iterations for Moore-Penrose inverses
Shwetabh Srivastava,D.K. Gupta 한국전산응용수학회 2014 Journal of applied mathematics & informatics Vol.32 No.1
A higher order iterative method to compute the Moore-Penrose inverses of arbitrary matrices using only the Penrose equation (ii) is developed by extending the iterative method described in [1]. Convergence properties as well as the error estimates of the method are studied. The efficacy of the method is demonstrated by working out four numerical examples, two involving a full rank matrix and an ill-conditioned Hilbert matrix, whereas, the other two involving randomly generated full rank and rank deficient matrices. The performance measures are the number of iterations and CPU time in seconds used by the method. It is observed that the number of iterations always decreases as expected and the CPU time first decreases gradually and then increases with the increase of the order of the method for all examples considered.
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An iterative method for orthogonal projections of generalized inverses
Shwetabh Srivastava,D.K. Gupta 한국전산응용수학회 2014 Journal of applied mathematics & informatics Vol.32 No.1
This paper describes an iterative method for orthogonal projections AA⍭ and A⍭A of an arbitrary matrix A, where A⍭ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If Zk k = 0, 1, 2, ... represents the k-th iterate obtained by our method then the sequence of the traces {trace(Zk)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace(I - Zk)} is a monotonically decreasing sequence converging to the nullity of A*.
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HIGHER ORDER ITERATIONS FOR MOORE-PENROSE INVERSES
Srivastava, Shwetabh,Gupta, D.K. The Korean Society for Computational and Applied M 2014 Journal of applied mathematics & informatics Vol.32 No.1
A higher order iterative method to compute the Moore-Penrose inverses of arbitrary matrices using only the Penrose equation (ii) is developed by extending the iterative method described in [1]. Convergence properties as well as the error estimates of the method are studied. The efficacy of the method is demonstrated by working out four numerical examples, two involving a full rank matrix and an ill-conditioned Hilbert matrix, whereas, the other two involving randomly generated full rank and rank deficient matrices. The performance measures are the number of iterations and CPU time in seconds used by the method. It is observed that the number of iterations always decreases as expected and the CPU time first decreases gradually and then increases with the increase of the order of the method for all examples considered.
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