The Explicit Spike Algorithm: Iterative Solution of the Reduced System
نویسنده
چکیده
The explicit SPIKE algorithm applies to narrow banded linear systems which are strictly diagonally dominant by rows. The parallel bottleneck is the solution of the so-called reduced system which is block tridiagonal and strictly diagonally dominant by rows. The reduced system can be solved iteratively using the truncated reduced system matrix as a preconditioner. In this paper we derive a tight estimate for the quality of this preconditioner.
منابع مشابه
An Explicit Viscosity Iterative Algorithm for Finding Fixed Points of Two Noncommutative Nonexpansive Mappings
We suggest an explicit viscosity iterative algorithm for finding a common element in the set of solutions of the general equilibrium problem system (GEPS) and the set of all common fixed points of two noncommuting nonexpansive self mappings in the real Hilbert space.
متن کاملIterative algorithm for the generalized $(P,Q)$-reflexive solution of a quaternion matrix equation with $j$-conjugate of the unknowns
In the present paper, we propose an iterative algorithm for solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} {underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$. By this iterative algorithm, the solvability of the problem can be determined automatically. When the matrix equation is consistent over...
متن کاملStrong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings
In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space with a uniformly G$hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(ell_{p})$ spaces, $1 < p
متن کاملUtilizing a new feed-back fuzzy neural network for solving a system of fuzzy equations
This paper intends to offer a new iterative method based on articial neural networks for finding solution of a fuzzy equations system. Our proposed fuzzied neural network is a ve-layer feedback neural network that corresponding connection weights to output layer are fuzzy numbers. This architecture of articial neural networks, can get a real input vector and calculates its corresponding fuzzy o...
متن کاملGlobal least squares solution of matrix equation $sum_{j=1}^s A_jX_jB_j = E$
In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...
متن کامل