Artículo
Abstract:
By means of successive partial substitutions, new fixed point linear equations can be obtained from old ones. The Jacobi method applied to a system in the sequence thus obtained constitutes a partial Gauss-Seidel method applied to the original one, and we analyze the behavior of the sequence of spectral radii of the successive iteration matrices (the modified Jacobi operators); we do this under the assumption that the starting operator is nonnegative with respect to a proper cone and has spectral radius less (or greater) than 1. Our main result is that, if the Jacobi operator obtained after k substitutions is irreducible, then the following one either is the same or has strictly smaller (or greater) spectral radius. This result implies that the whole sequence of spectral radii is monotone. © 1983.
Registro:
| Documento: | Artículo |
| Título: | On modified Jacobi linear operators |
| Autor: | Milaszewicz, J.P. |
| Filiación: | Departamento de Matemática Facultad de Ciencias Exactas y Naturales Ciudad Universitaria, 1428 Buenos Aires, Argentina |
| Año: | 1983 |
| Volumen: | 51 |
| Número: | C |
| Página de inicio: | 127 |
| Página de fin: | 136 |
| DOI: | http://dx.doi.org/10.1016/0024-3795(83)90153-2 |
| 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_v51_nC_p127_Milaszewicz |
Referencias:
- Berman, Plemmons, (1979) Nonnegative Matrices in the Mathematical Sciences, , Academic, New York
- Milaszewicz, On criticality and the Stein-Rosenberg theorem (1981) SIAM Journal on Numerical Analysis, 18, pp. 559-564
- Milaszewicz, On fixed point linear equations (1981) Numer. Math., 38, pp. 53-59
- Rheinboldt, Vandergraft, A simple approach to the Perron-Frobenius theory for positive operators in general partially-ordered finite-dimensional linear spaces (1973) Mathematics of Computation, 27, pp. 139-145
- Robert, Algorithmes tronqués de découpe linéaire (1972) RAIRO, revue de l'AFCET, pp. 45-64
- Robert, Autour du théoreme de Stein-Rosenberg (1976) Numer. Math., 27, pp. 133-141
- Varga, (1962) Matrix Iterative Analysis, , Prentice-Hall, Englewood Cliffs, N.J
Citas:
---------- APA ----------
(1983) . On modified Jacobi linear operators. Linear Algebra and Its Applications, 51(C), 127-136.http://dx.doi.org/10.1016/0024-3795(83)90153-2
---------- CHICAGO ----------
Milaszewicz, J.P. "On modified Jacobi linear operators" . Linear Algebra and Its Applications 51, no. C (1983) : 127-136.http://dx.doi.org/10.1016/0024-3795(83)90153-2
---------- MLA ----------
Milaszewicz, J.P. "On modified Jacobi linear operators" . Linear Algebra and Its Applications, vol. 51, no. C, 1983, pp. 127-136.http://dx.doi.org/10.1016/0024-3795(83)90153-2
---------- VANCOUVER ----------
Milaszewicz, J.P. On modified Jacobi linear operators. Linear Algebra Its Appl. 1983;51(C):127-136.http://dx.doi.org/10.1016/0024-3795(83)90153-2
