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Computing the nearest diagonally dominant matrix
Author(s) -
Mendoza María,
Raydan Marcos,
Tarazaga Pablo
Publication year - 1998
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199811/12)5:6<461::aid-nla141>3.0.co;2-v
Subject(s) - diagonally dominant matrix , mathematics , diagonal , projection (relational algebra) , subspace topology , matrix (chemical analysis) , combinatorics , cone (formal languages) , diagonal matrix , algorithm , pure mathematics , geometry , mathematical analysis , materials science , composite material , invertible matrix
We solve the problem of minimizing the distance from a given matrix to the set of symmetric and diagonally dominant matrices. First, we characterize the projection onto the cone of diagonally dominant matrices with positive diagonal, and then we apply Dykstra's alternating projection algorithm on this cone and on the subspace of symmetric matrices to obtain the solution. We discuss implementation details and present encouraging preliminary numerical results. Copyright © 1999 John Wiley & Sons, Ltd.