Primal and polar approach for computing the symmetric diagonally dominant projection

Numerical Linear Algebra with Applications

Volumn 9, Issue 5, 2002, Pages 333-345

  Raydan, Marcos ^a   Tarazaga, Pablo ^b  

^a FACULTAD DE CIENCIAS   (Venezuela)

^b UNIVERSITY OF PUERTO RICO   (Puerto Rico)

Author keywords

Diagonally dominant matrices; Dykstra's algorithm; Kuhn Tucker conditions; Moreau's theorem; Polyhedral cones

Indexed keywords

EID: 0043184621     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.277     Document Type: Article

References (14)

1. Mendoza M, Raydan M, Tarazaga P. Computing the nearest diagonally dominant matrix. Numerical Linear Algebra with Applications 1998; 5:461-474.
2. Boyle JP, Dykstra RL. A method for finding projections onto the intersections of convex sets in Hubert spaces. Lecture Notes in Statistics 1986; 37:28-47.
3. Dykstra RL. An algorithm for restricted least-squares regression. Journal of the American Statistical Association 1983; 78:837-842.
4. Barker GP. Theory of cones. Linear Algebra and its Applications 1981; 39:263-291.
5. Barker GP, Carlson D. Cones of diagonally dominant matrices. Pacific Journal of Mathematics 1975; 57:15-32.
6. Barker GP, Loewy R. The structure of cones of matrices. Linear Algebra and its Applications 1975; 12:87-94.
7. Fiedler M, Ptak V. Diagonally dominant matrices. Czechoslovak Mathematical Journal 1967; 17(92):420-433.
8. Dahl G. A note on diagonally dominant matrices. Linear Algebra and its Applications 2000; 317:217-224.
9. Stoer J, Witzgall C. Convexity and Optimization in Finite Dimensions I. Springer: Berlin, 1970.
10. Luenberger DO. Optimization by Vector Space Methods. Wiley, Inc: New York, 1969.
11. Moreau JJ. Décomposition orthogonale d'un espace hilbertien selon deux cônes mutuellement polaires. Comptes Rendus de L'académie des Sciences de Paris 1962; 255:238-240.
12. Raydan M, Tarazaga P. Computing the symmetric diagonally dominant projection via duality. In Proceedings of XV SWIM, University of Puerto Rico, Caceres LF, Barety JE, Ramos M. (eds). 2000; 59-76.
13. Avriel M. Nonlinear Programming: Analysis and Methods. Prentice-Hall: Englewood Cliffs, NJ, 1976.
14. Deutsch F, Hundal H. The rate of convergence of Dykstra's cyclic projections algorithm: the polyhedral case. Numerical Functional Analysis and Optimization 1994; 15:537-565.