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|Title:||Solving sparse linear systems by an abs-method that corresponds to LU-decomposition|
AMS classification: 65F50, 65F05
|Source:||Phua, K.H. (1988-09). Solving sparse linear systems by an abs-method that corresponds to LU-decomposition. BIT 28 (3) : 709-718. ScholarBank@NUS Repository. https://doi.org/10.1007/BF01941145|
|Abstract:||Abaffy, Broyden, and Spedicato (ABS) have recently proposed a class of direct methods for solving nonsparse linear systems. It is the purpose of this paper to demonstrate that with proper choice of parameters, ABS methods exploit sparsity in a natural way. In particular, we study the choice of parameters which corresponds to an LU-decomposition of the coefficient matrix. In many cases, the fill-in, represented by the nonzero elements of the deflection matrix, uses less storage than the corresponding fill-in of an explicit LU factorization. Hence the above can be a viable and simple method for solving sparse linear systems. A simple reordering scheme for the coefficient matrix is also proposed for the purpose of reducing fill-in of the deflection matrices. © 1988 BIT Foundations.|
|Appears in Collections:||Staff Publications|
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