Parallel Algorithms for Nonlinear Problems
R. E. White · SIAM Journal on Algebraic and Discrete Methods · 1986
Multi-splittings of a matrix are used to generate parallel algorithms to approximate the solutions of nonlinear algebraic systems. A parallel nonlinear Gauss–Seidel algorithm for approximating the solution of $Au + \phi ( u ) = f$ where A is an M-matrix is introduced and studied. Also, a parallel Newton–SOR method is defined for the problem $F ( u ) = 0$ where $F' ( u ) = $ the Jacobian is an M-matrix. An illustration and comparison of these methods with their serial versions is given. The speed-up on the Denelcor HEP parallel processing computer is also recorded.