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Title of article :
Dykstraʹs algorithm for constrained least-squares rectangular matrix problems
Author/Authors :
Carlos R. Escalante، نويسنده , , M. Raydan، نويسنده ,
Issue Information :
هفته نامه با شماره پیاپی سال 1997
Pages :
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Abstract :
In a recent paper, the authors applied Dykstraʹs alternating projection algorithm to solve constrained least-squares n × n matrix problems. We extend these results in two different directions. First, we make use of the singular value decomposition to solve now constrained least-squares rectangular m × n matrix problems that arise in several applications. Second, we propose a new and improved implementation of the projection algorithm onto the -positive definite set of matrices. This implementation does not require the computation of all eigenvalues and eigenvectors of a matrix per iteration, and still guarantees convergence. Finally, encouraging preliminary numerical results are discussed.
Keywords :
Alternating projection methods , Dykstraיs algorithm , Constrained least-squares , Gerschgorin circles , Singular value descomposition
Journal title :
Computers and Mathematics with Applications
Serial Year :
Link To Document :