Block Iterative Algorithms for Solving Hermite Bicubic Collocation Equations
In this paper, we present a so-called local elimination technique by which a nonsymmetric system arising in the discretization of the Poisson equation with a Hermite bicubic collocation approximation is reduced to a block tridiagonal and "block symmetric" system. A class of block iterative...
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| Veröffentlicht in: | SIAM journal on numerical analysis Jg. 33; H. 2; S. 589 - 601 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.04.1996
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| ISSN: | 0036-1429, 1095-7170 |
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| Abstract | In this paper, we present a so-called local elimination technique by which a nonsymmetric system arising in the discretization of the Poisson equation with a Hermite bicubic collocation approximation is reduced to a block tridiagonal and "block symmetric" system. A class of block iterative algorithms is developed for solving the resulting system. The convergence rates of algorithms are discussed. |
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| AbstractList | In this paper, we present a so-called local elimination technique by which a nonsymmetric system arising in the discretization of the Poisson equation with a Hermite bicubic collocation approximation is reduced to a block tridiagonal and "block symmetric" system. A class of block iterative algorithms is developed for solving the resulting system. The convergence rates of algorithms are discussed. |
| Author | Sun, W. |
| Author_xml | – sequence: 1 givenname: W. surname: Sun fullname: Sun, W. |
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| Cites_doi | 10.1137/0724006 10.1137/0721047 10.1090/S0025-5718-1983-0717699-0 10.1137/0713073 10.1016/B978-0-12-100560-3.50036-6 10.1137/0729010 10.1016/0024-3795(83)90142-8 10.1145/6187.6191 10.1137/0728038 10.1007/978-1-4612-5018-0 10.1007/BF01385789 10.1016/0016-0032(89)90076-8 10.1016/S0378-4754(98)90001-5 |
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| Copyright | Copyright 1996 Society for Industrial and Applied Mathematics 1996 INIST-CNRS [Copyright] © 1996 Society for Industrial and Applied Mathematics |
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| Keywords | Numerical approximation Convergence rate Poisson equation Iterative method Collocation method Algorithm Partial differential equation Discretization method Spline approximation |
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| References | R2 R3 R4 R5 R6 R7 Hageman Louis A. (R8) 1981 Varga Richard S. (R17) 1962 R10 R12 R11 R13 R16 R15 Prenter P. M. (R14) 1975 R1 |
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| SubjectTerms | Algorithms Applied mathematics Boundary conditions Difference equations Eigenvalues Elliptic differential equations Exact sciences and technology Fast Fourier transformations Fourier transforms Iterative methods Linear systems Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Partial differential equations Partial differential equations, boundary value problems Poisson equation Sciences and techniques of general use Tensors Textual collocation |
| Title | Block Iterative Algorithms for Solving Hermite Bicubic Collocation Equations |
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