SYMMLQ-like procedure for Ax = b where A is a special normal matrix

Calcolo

Volumn 43, Issue 1, 2006, Pages 17-37

  Fassbender, H ^a   Ikramov, Kh D ^b  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Generalized Krylov sequence; GMRES algorithm; Normal matrix; Rayleigh Ritz projection; SYMMLQ algorithm

Indexed keywords

DEGREE CURVES; GENERALIZED KRYLOV SEQUENCE; GMRES ALGORITHM; LANCZOS; NORMAL MATRIX; RAYLEIGH-RITZ; RAYLEIGH-RITZ PROJECTION; RITZ PROJECTION; SPECTRA'S; SYMMLQ ALGORITHM;

LINEAR SYSTEMS;

EID: 33750902206     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10092-006-0112-x     Document Type: Article

References (14)

1. Barth, T., Manteuffel, T.A.: Multiple recursion conjugate gradient algorithms. I. Sufficient conditions. SIAM J. Matrix Anal. Appl. 21, 768-796 (2000)
2. Elsner, L., Ikramov, Kh.D.: On a condensed form for normal matrices under finite sequences of elementary unitary similarities. Linear Algebra Appl. 254, 79-98 (1997)
3. Faber, V., Manteuffel, T.A.: Necessary and sufficient conditions for the existence of a conjugate gradient method. SIAM J. Numer. Anal. 21, 352-362 (1984)
4. Gragg, W.B.: Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle. J. Comput. Appl. Math. 46, 183-198 (1993)
5. Huhtanen, M.: Combining normality with the FFT techniques. (Helsinki Univ. of Technology Inst. of Math. Research Reports A451) Helsinki: Helsinki Univ. of Technology 2003
6. Huhtanen, M.: A Hermitian Lanczos method for normal matrices. SIAM J. Matrix Anal. Appl. 23, 1092-1108 (2002)
7. Huhtanen, M.: Orthogonal polyanalytic polynomials and normal matrices. Math. Comp. 72, 355-373 (2002)
8. Huhtanen, M., Larsen, R.M.: Exclusion and inclusion regions for the eigenvalues of a normal matrix. SIAM J. Matrix Anal. Appl. 23, 1070-1091 (2002)
9. Jagels, C.F., Reichel, L.: A fast minimal residual algorithm for shifted unitary matrices. Numer. Linear Algebra Appl. 1, 555-570 (1994)
10. Paige, C.C., Saunders, M.A.: Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12, 617-629 (1975)
11. Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7, 856-869 (1986)
12. Voevodin, V.V.: The question of non-self-adjoint extension of the conjugate gradient method is closed. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 23, 477-479 (1983);
13. transl.: USSR Comput. Math. Phys. 23 (2), 143-144 (1983)
14. Voevodin, V.V., Tyrtyshnikov, E.E.: On a generalization of conjugate direction methods. In: Voevodin, V. V. (ed.): Numerical methods of algebra. A collection of papers. Moscow: Izdat. Moskosk Univ. 1981, pp. 3-9