Journal
THEORETICAL COMPUTER SCIENCE
Volume 411, Issue 31-33, Pages 2818-2826Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.tcs.2010.04.011
Keywords
Alternating projection method; Doubly symmetric matrix; Least-squares problem; Singular value decomposition
Categories
Funding
- National Natural Science Foundation of China [10571047, 10861008]
- Doctorate Foundation of the Ministry of Education of China [20060532014]
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In this work we apply Dykstra's alternating projection algorithm for minimizing parallel to AX - B parallel to where parallel to . parallel to is the Frobenius norm and A is an element of R(mxn), B is an element of R(mxn) and X is an element of R(nxn) are doubly symmetric positive definite matrices with entries within prescribed intervals. We first solve the constrained least-squares matrix problem by using the special structure properties of doubly symmetric matrices, and then use the singular value decomposition to transform the original problem into a simpler one that fits nicely with the algorithm originally developed by [R. Escalante, M. Raydan, Dykstra's algorithm for a constrained least-squares matrix problem, Numer. Linear Algebra Appl. 3 (1996) 459-471]. (C) 2010 Elsevier B.V. All rights reserved.
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