TY - GEN
T1 - Matrix inverse-free algorithms for the general eigenvalue problem
AU - Hasan, Mohammed A
AU - Hasan, A. A.
PY - 2001/12/1
Y1 - 2001/12/1
N2 - There are numerous applications in sciences, engineering and mathematics that give rise to problems involving the computation of orthogonal projections onto selective invariant subspaces of matrices. Conventional algorithms for subspace estimation based upon eigenvalue decomposition (EVD) or singular value decomposition (SVD) are, however, both expensive to compute, and difficult to make recursive or implement in parallel. In contrast, algorithms based on the QR factorization have established pipelinable architectures. In this paper, we introduce novel matrix-inverse free algorithms for block matrix decomposition. They involve a combination of Newton's method and the QR factorization. Some of these methods can be shown to have cubic or quadratic convergence rates, while others can be of any desirable convergent rate.
AB - There are numerous applications in sciences, engineering and mathematics that give rise to problems involving the computation of orthogonal projections onto selective invariant subspaces of matrices. Conventional algorithms for subspace estimation based upon eigenvalue decomposition (EVD) or singular value decomposition (SVD) are, however, both expensive to compute, and difficult to make recursive or implement in parallel. In contrast, algorithms based on the QR factorization have established pipelinable architectures. In this paper, we introduce novel matrix-inverse free algorithms for block matrix decomposition. They involve a combination of Newton's method and the QR factorization. Some of these methods can be shown to have cubic or quadratic convergence rates, while others can be of any desirable convergent rate.
UR - http://www.scopus.com/inward/record.url?scp=0034998663&partnerID=8YFLogxK
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U2 - 10.1109/ISCAS.2001.921320
DO - 10.1109/ISCAS.2001.921320
M3 - Conference contribution
AN - SCOPUS:0034998663
SN - 0780366859
SN - 9780780366855
T3 - ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings
SP - 353
EP - 356
BT - ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings
T2 - 2001 IEEE International Symposium on Circuits and Systems, ISCAS 2001
Y2 - 6 May 2001 through 9 May 2001
ER -