Convergence of a Two Stage Richardson Iterative Procedure for Solving Systems of
Convergence of a Two Stage Richardson Iterative Procedure for Solving Systems of
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14 ), (1 . 13) and (1. 7) . Q Note that if 6 = e =, we have p = p and Theorem 1 reduces to the standard convergence property of the second-order Richardson method (see Golub and Varga (1961) ) . We also note that it is possible to choose the first iterate x, in such a way that the error bound of Theorem 1 is somewhat reduced.
- 8 - 1 . 2 Optimal parameters .
There are three free parameters in Method 1, namely 5, a and lo. Let us first suppose that 6 =0, so that the inner systems (1. 4) are solv...ed exactly. In this case the optimal choices of a and to/ i. E. Those that minimize p in (1. 14), may be described using Young's theory of successive overrelaxation. Let ; - I 0^ I = max ] a. | j - -- where {a. } are the eigenvalues of K = I-oM A, as before. Given any a» -' 1 the optimal choice of lo is obtained by choosing A, = X„ = ^coo „ in (1. 13), i. E.
oj = ^ . (1. 21) 1 + A-a^ It can be verified that this choice results in P = 1^1, J = 1^1, jl = l^2.. Jl = I'^l'^il = "^^^ for all j, j = l, ...
What to read after Convergence of a Two Stage Richardson Iterative Procedure for Solving Systems of?
You can find similar books in the "Read Also" column, or choose other free books by Gene H Golub to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
14 ), (1 . 13) and (1. 7) . Q Note that if 6 = e =, we have p = p and Theorem 1 reduces to the standard convergence property of the second-order Richardson method (see Golub and Varga (1961) ) . We also note that it is possible to choose the first iterate x, in such a way that the error bound of Theorem 1 is somewhat reduced.
- 8 - 1 . 2 Optimal parameters .
There are three free parameters in Method 1, namely 5, a and lo. Let us first suppose that 6 =0, so that the inner systems (1. 4) are solv...ed exactly. In this case the optimal choices of a and to/ i. E. Those that minimize p in (1. 14), may be described using Young's theory of successive overrelaxation. Let ; - I 0^ I = max ] a. | j - -- where {a. } are the eigenvalues of K = I-oM A, as before. Given any a» -' 1 the optimal choice of lo is obtained by choosing A, = X„ = ^coo „ in (1. 13), i. E.
oj = ^ . (1. 21) 1 + A-a^ It can be verified that this choice results in P = 1^1, J = 1^1, jl = l^2.. Jl = I'^l'^il = "^^^ for all j, j = l, ...
What to read after Convergence of a Two Stage Richardson Iterative Procedure for Solving Systems of?
You can find similar books in the "Read Also" column, or choose other free books by Gene H Golub to read onlineMoreLess
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