# On the choice of iteration parameters in the Stone incomplete factorization

Aplikace matematiky (1983)

- Volume: 28, Issue: 4, page 295-306
- ISSN: 0862-7940

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topSegeth, Karel. "On the choice of iteration parameters in the Stone incomplete factorization." Aplikace matematiky 28.4 (1983): 295-306. <http://eudml.org/doc/15307>.

@article{Segeth1983,

abstract = {The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values of the parameters successfully without a deeper a priori analysis of the linear system solved.},

author = {Segeth, Karel},

journal = {Aplikace matematiky},

keywords = {Stone incomplete factorization; choice of parameters; Stone’s method; large sparse systems; Numerical experiments; Stone incomplete factorization; choice of parameters; Stone's method; large sparse systems; Numerical experiments},

language = {eng},

number = {4},

pages = {295-306},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On the choice of iteration parameters in the Stone incomplete factorization},

url = {http://eudml.org/doc/15307},

volume = {28},

year = {1983},

}

TY - JOUR

AU - Segeth, Karel

TI - On the choice of iteration parameters in the Stone incomplete factorization

JO - Aplikace matematiky

PY - 1983

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 28

IS - 4

SP - 295

EP - 306

AB - The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values of the parameters successfully without a deeper a priori analysis of the linear system solved.

LA - eng

KW - Stone incomplete factorization; choice of parameters; Stone’s method; large sparse systems; Numerical experiments; Stone incomplete factorization; choice of parameters; Stone's method; large sparse systems; Numerical experiments

UR - http://eudml.org/doc/15307

ER -

## References

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- K. Segeth, The iterative use of fast algorithms for the solution of elliptic partial differential equations, (Lecture at the summer school Software a algoritmy numerické matematiky 4, Karlovy Vary 1981.) Matematický ústav ČSAV, Praha 1983. (1981)
- K. Segeth, Numerical experiments with the Stone incomplete triangular decomposition, Mathematical Models in Physics and Chemistry and Their Numerical Realization 3. (School-Seminar, Visegrád 1982.) To appear. (1982) MR0790545
- S.Selberherr A.Schütz W. Petzl, 10.1109/JSSC.1980.1051444, IEEE J. Solid-State Circuits SC-15 (1980), 605-623. (1980) DOI10.1109/JSSC.1980.1051444
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- R. J. Taranto, Numerical studies of Stone’s factorization and the iteration parameters, $\alpha $ and $\tau $, Rep. 423, Dept. of Computer Science, University of Illinois, Urbana, 111., 1971. (1971)

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