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Performance analysis and implementation of gauss-huard elimination 1.
| Content Provider | CiteSeerX |
|---|---|
| Abstract | this paper, we give a block algorithm for the Gauss-Huard elimination. For distributed memory systems, a performance analysis of this block algorithm is given and compared with results on two distributed memory systems: the MEIKO Computing Surface and the Parsytec#GCel. Results for Huard's algorithm on the MEIKO are compared with results for Gaussian elimination [Hoffmann91]. To reduce cache-operations in shared-memory systems, Hoffmann introduced a variant of the block Gauss-Huard algorithm: the twined block algorithm [Hoffmann93]. For this block algorithm, a performance analysis for shared-memory systems with cache is given. For large n, Gauss-Huard elimination may be faster than Gaussian elimination on shared memory computers. Further research is still going on. More work about the numerical stability and/or implementation of Huard's algorithm can be found in: [Huard76], [Cosnard86], [Dekker89], [Hoffmann89], [Potma89], [Dekker93], [Potma93] and [Rijnierse93]. Performance analysis and implementation of Gauss-Huard elimination 2 1 Gaussian and Gauss-Jordan elimination Given an n-th order non-singular matrix A and right-hand side vector b, we want to solve the linear system A x = b to obtain a result vector x. For this solution, Gaussian elimination is still the most popular method. With Gauss-Jordan elimination a diagonal matrix results. The main difference between Gaussian elimination and Gauss-Jordan is that the latter algorithm obtains the explicit inverse of matrix U by calculation of the factorisation. This has influences for the numerical stability of the Gauss-Jordan algorithm. Dekker et al. has in detail described the error analysis of both algorithms [Dekker93]. In this chapter we will give a short description of Gaussian and Gauss-Jordan elimination, becau... |
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| Access Restriction | Open |
| Subject Keyword | Gauss-huard Elimination Performance Analysis Gaussian Elimination Block Algorithm Distributed Memory System Shared-memory System Numerical Stability Gauss-jordan Elimination Linear System Right-hand Side Vector N-th Order Non-singular Matrix Meiko Computing Surface Block Gauss-huard Algorithm Error Analysis Diagonal Matrix Result Latter Algorithm Popular Method Algorithm Dekker93 Memory Computer Parsytec Gcel Main Difference Gauss-jordan Algorithm Short Description Twined Block Algorithm Hoffmann93 Gauss-jordan Elimination Given Result Vector Explicit Inverse Gaussian Elimination Hoffmann91 |
| Content Type | Text |
| Resource Type | Article |
