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Dykstra's algorithm for constrained least-squares rectangular matrix problems

✍ Scribed by R. Escalante; M. Raydan

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
404 KB
Volume
35
Category
Article
ISSN
0898-1221

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✦ Synopsis

ln a recent paper, the authors applied Dykstra's alternating projection algorithm to solve constrained least-squares n x n matrix problems. We extend these results in two different directions. First, we make use of the singular value decomposition to solve now constrained leastsquares rectangular m x n matrix problems that arise in several applications. Second, we propose a new and improved implementation of the projection algorithm onto the e-positive definite set of matrices. This implementation does not require the computation of all elgenvalues and eigenvectors of a matrix per iteration, and still guarantees convergence. Finally, encouraging preliminary numerical results are discussed.

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