Study on semi-conjugate direction methods for non-symmetric systems

International Journal for Numerical Methods in Engineering

Volumn 60, Issue 8, 2004, Pages 1383-1399

  Dai, Yu Hong ^a   Yuan, Jinyun ^b  

^a Chinese Academy of Mathematics and System Science   (China)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

Author keywords

Breakdown; Conjugate gradient method; Existence; Left conjugate direction; Left conjugate direction method; Limited memory left conjugate direction method; Linear system; Non singular matrix; Semi conjugate direction

Indexed keywords

ALGORITHMS; MATRIX ALGEBRA; PROBLEM SOLVING;

SEMI-CONJUGATE DIRECTION METHOD; SKEW-SYMMETRIC MATRICES;

LINEAR SYSTEMS;

MATHEMATICAL METHOD;

EID: 3142570750     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.983     Document Type: Article

References (8)

1. Yuan JY, Golub GH, Plemmons RJ, Cecilio WAG. Semi-conjugate direction methods for real positive definite systems. BIT 2004; 44:189-207.
2. Hestenes MR, Stiefel E. The method of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards 1952; 49:409-436.
3. Stewart GW. Conjugate direction methods for solving systems of linear equations. Numerische Mathematik 1973; 21-285-297.
4. Renato S. Silva, Fernanda MP, Raupp Regina C. Almeida. A numerical methodolgy to solve thermal pollution problems. IX Congresso Brasileiro de Engenharia e Cincias Trmicas, Caxambu, Brazil, 2002 (http://www.Incc.br/proj-pesq/relpesq-02.html/32/2002).
5. Faber V, Manteuffel T. Necessary and sufficient conditions for the existence of a conjugate gradient method. SIAM Journal on Numerical Analysis 1984; 21:352-362.
6. Liu DC, Nocedal J. On the limited memory BFGS method for large scale optimization. Mathematical Programming 1989; 45:503-528.
7. Calvetti D, Golub GH, Reichel L. Adaptive Chebyshev iterative methods for non-symmetric linear systems based on modified moments. Numerische Mathematik 1994; 67:21-40.
8. Bai ZZ, Golub GH, NG MK. Hermitian and skew-Hermitian splitting methods for non-Hermitian positive linear systems. SIAM Journal on Matrix Analysis and Applications 2003; 24:603-626.