Optimized cyclic reduction for the solution of linear tridiagonal systems on parallel computers
نویسندگان
چکیده
منابع مشابه
A parallel solver for tridiagonal linear systems for distributed memory parallel computers
Brugnano, L_, A parallel solver for tridiagonal linear systems for distributed memory parallel computers, Parallel Computing 17 (1991) 1017-1023. The solution of linear tridiagonal systems is a very common problem in Numerical Analysis. Many algorithms are known for solving such linear systems on vector and parallel computers [3,4,6-9]. In this paper a new parallel method is presented, which is...
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All numerical techniques for the solution of Partial Differential Equations (PDE) involve discretization. Many times this discretization leads to the solution of a large system of linear equations, the generic of which can be represented as Ax = D; A is known as the coefficient matrix , while x is the vector of unknowns and D is the right-hand side vector. It often happens that the coefficient ...
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24 restriction. As and , the minimum of δ (l) is achieved on the boundary of R. It is not difficult to see that this minimum is in x = y = , independently of the values of the greek letters. With this, we can see that: Now, if , we have: which allows to finish the proof: x y , () R ∈ 0 δ l 1 − () 1 − , [ ] 0 δ l 1 − () 1 − , [ ] × = x ∂ ∂δ l () 0 ≠ y ∂ ∂δ l () 0 ≠ δ l 1 − () 1 − δ l () δ l 1 − ...
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Tridiagonal systems play a fundamental role in matrix computation. In particular, in recent years parallel algorithms for the solution of tridiagonal systems have been developed. Among these, the cyclic reduction algorithm is particularly interesting. Here the stability of the cyclic reduction method is studied under the assumption of diagonal dominance. A backward error analysis is made, yield...
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The problem of solving tridiagonal systems on parallel machines has been studied extensively. This paper examines an existing parallel solvers for tridiagonal systems and extends this divide-and-conquer algorithm to solving almost-tridiagonal systems, systems consisting of a tridiagonal matrix with non-zeros elements in the upper right and lower left corners. In addition to a sketch of a solver...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1993
ISSN: 0898-1221
DOI: 10.1016/0898-1221(93)90109-9