Evolutionary factorization and superfast relaxation count
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Systems of linear algebraic equations with strongly rarefied matrices of enormous size appear in finite-difference solving of multidimensional elliptic equations. These systems are solved by iteration methods that converge rather slowly. For rectangular grids with variable coefficients and net steps, a considerably faster method is proposed. In the case of difference schemes for parabolic equations, a cost effective method called evolutionary factorization is developed. For elliptic equations, a relaxation count by evolutionally factorized schemes is suggested. This iteration method has the logarithmic convergence speed. A set of steps that practically optimizes the convergence of this algorithm and a procedure to regulate the steps that resembles the Richardson method are proposed. The procedure allows one to obtain an a posteriori asymptotically accurate error estimate of the iteration process. Previously such estimates for iteration processes were not known.
Keywordsevolutionary factorization logarithmic relaxation count
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- 1.A. A. Samarskii and V. B. Andreev, Difference Methods for Elliptic Equations (Nauka, Moscow, 1976) [in Russian].Google Scholar
- 2.A. A. Samarskii and E. S. Nikolaev, Methods for Solving Network Equations (Nauka, Moscow, 1978) [in Russian].Google Scholar
- 3.D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra (FIZMATGIZ, Moscow, 1963) [in Russian].Google Scholar
- 5.N. N. Yanenko, Fractional Step Method for Solving Multidimensional Problems of Mathematical Fhysics (Nauka, Novosibirsk, 1967) [in Russian].Google Scholar
- 6.A. A. Samarskii, Theory of Difference Schemes (Nauka, Moscow, 1989) [in Russian].Google Scholar
- 8.N. N. Kalitkin, Numerical Methods (Nauka, Moscow, 1978) [in Russian].Google Scholar