论文信息 - Multitasking Algorithms on CRAY Computers for Interval Arithmetic Newton-Like Methods for a Class of Systems of Nonlinear Equations

Multitasking Algorithms on CRAY Computers for Interval Arithmetic Newton-Like Methods for a Class of Systems of Nonlinear Equations

For several classes of systems of nonlinear equations interval arithmetic methods can be defined which converge to a solution essentially under the condition that an initial inclusion is known, i.e. the convergence can be said to be global. We consider vector algorithms for an interval arithmetic Newton-like method which is combined with an interval arithmetic “fast solver” for nonlinear systems with block tridiagonal Jacobian. As an example we consider a nine point discretization of a twodimensional nonlinear Dirichlet problem. More specifically we discuss efficient algorithms for multiprocessor computers with two and four vector processors. The algorithms are intended to use all processors in parallel as far as possible under the condition that the vector efficiency in the parallel tasks does not substantially decrease. We report numerical results for programs using the multitasking routines on 1 and 2-processor CRAY-X/MP.

Hartmut Schwandt

[1] Hartmut Schwandt. Almost globally convergent interval methods for discretizations of nonlinear elliptic partial differential equations , 1986 .

[2] H. Schwandt. Newton-like interval methods for large nonlinear systems of equations on vector computers , 1985 .

[3] Jack J. Dongarra,et al. Multiprocessing linear algebra algorithms on the CRAY X-MP-2: Experiences with small granularity , 1984, J. Parallel Distributed Comput..

[4] Hartmut Schwandt. An Interval Arithmetic Approach for the Construction of an Almost Globally Convergent Method for the Solution of the Nonlinear Poisson Equation on the Unit Square , 1984 .

[5] Roger W. Hockney,et al. (r∞, n1/2, s1/2) measurements on the 2-CPU CRAY X-MP , 1985, Parallel Comput..

[6] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[7] Hartmut Schwandt,et al. The Solution of Nonlinear Elliptic Dirichlet Problems on Rectangles by Almost Globally Convergent Interval Methods , 1985 .