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Abstract:

When convergent Jacobi or Gauss-Seidel iterations can be applied to solve systems of linear equations, a natural question is how convergence rates are affected if the original system is modified by performing some Gaussian elimination. We prove that if the initial iteration matrix is nonnegative, then such elimination improves convergence. Our results extend those contained in [4]. © 1987.

Registro:

Documento: Artículo
Título:Improving Jacobi and Gauss-Seidel Iterations
Autor:Milaszewicz, J.P.
Filiación:Departamento de Matemática Facultad de Ciencias Exactas y Naturales Ciudad Universitaria, 1428 Buenos Aires, Argentina
Año:1987
Volumen:93
Número:C
Página de inicio:161
Página de fin:170
DOI: http://dx.doi.org/10.1016/S0024-3795(87)90321-1
Título revista:Linear Algebra and Its Applications
Título revista abreviado:Linear Algebra Its Appl
ISSN:00243795
CODEN:LAAPA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v93_nC_p161_Milaszewicz

Referencias:

  • Funderlic, Mankin, Solution of Homogeneous Systems of Linear Equations Arising from Compartmental Models (1981) SIAM Journal on Scientific and Statistical Computing, 2, pp. 375-383
  • Funderlic, Plemmons, LU decomposition of M-matrices by elimination without pivoting (1981) Linear Algebra Appl., 41, pp. 99-110
  • George, Liu, (1981) Computer Solution of Large Sparse Positive Definite Systems, , Prentice-Hall, Englewood Cliffs, N.J
  • Juncosa, Mulliken, On the Increase of Convergence Rates of Relaxation Procedures for Elliptic Partial Difference Equations (1960) Journal of the ACM, 7, pp. 29-36
  • Milaszewicz, A generalization of the Stein-Rosenberg theorem to Banach spaces (1980) Numer. Math., 34, pp. 403-409
  • Milaszewicz, On modified Jacobi linear operators (1983) Linear Algebra Appl., 51, pp. 127-136
  • Robert, Algorithmes tronqués de découpe linéaire (1972) RAIRO, pp. 45-64. , revue de l'AFCET
  • Robert, Autour du théorème de Stein-Rosenberg (1976) Numer. Math., 27, pp. 133-141
  • Varga, (1962) Matrix Iterative Analysis, , Prentice-Hall, Englewood Cliffs, N.J

Citas:

---------- APA ----------
(1987) . Improving Jacobi and Gauss-Seidel Iterations. Linear Algebra and Its Applications, 93(C), 161-170.
http://dx.doi.org/10.1016/S0024-3795(87)90321-1
---------- CHICAGO ----------
Milaszewicz, J.P. "Improving Jacobi and Gauss-Seidel Iterations" . Linear Algebra and Its Applications 93, no. C (1987) : 161-170.
http://dx.doi.org/10.1016/S0024-3795(87)90321-1
---------- MLA ----------
Milaszewicz, J.P. "Improving Jacobi and Gauss-Seidel Iterations" . Linear Algebra and Its Applications, vol. 93, no. C, 1987, pp. 161-170.
http://dx.doi.org/10.1016/S0024-3795(87)90321-1
---------- VANCOUVER ----------
Milaszewicz, J.P. Improving Jacobi and Gauss-Seidel Iterations. Linear Algebra Its Appl. 1987;93(C):161-170.
http://dx.doi.org/10.1016/S0024-3795(87)90321-1