For a class of ideal models of parallel computers, we define some measuring parameters such as the speed-up, the efficiency, the redundancy of a linear and nonlinear parallel iteration method in both average and asymp...For a class of ideal models of parallel computers, we define some measuring parameters such as the speed-up, the efficiency, the redundancy of a linear and nonlinear parallel iteration method in both average and asymptotic senses, as well as the utilization ratio of the parallel computer. These parameters are reasonable and convenient for the theoretical studies of the parallel iteration methods.展开更多
Parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations Aψ (x)+Tψ(x) = b, with A, T L(Rn) beingmatrices of particular properties, : Rn→ Rn being diagonal ...Parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations Aψ (x)+Tψ(x) = b, with A, T L(Rn) beingmatrices of particular properties, : Rn→ Rn being diagonal and continuousmappings, and b ∈ Rn a known vector; and their global convergence are investigated in detail under weaker conditions. Some numerical computations show thatthe new methods have better convergence properties than the known ones in theliterature.展开更多
文摘For a class of ideal models of parallel computers, we define some measuring parameters such as the speed-up, the efficiency, the redundancy of a linear and nonlinear parallel iteration method in both average and asymptotic senses, as well as the utilization ratio of the parallel computer. These parameters are reasonable and convenient for the theoretical studies of the parallel iteration methods.
文摘Parallel multisplitting nonlinear iterative methods are established for the system of nonlinear algebraic equations Aψ (x)+Tψ(x) = b, with A, T L(Rn) beingmatrices of particular properties, : Rn→ Rn being diagonal and continuousmappings, and b ∈ Rn a known vector; and their global convergence are investigated in detail under weaker conditions. Some numerical computations show thatthe new methods have better convergence properties than the known ones in theliterature.
