Parallel Tensor Methods for Nonlinear Equations and Nonlinear Least Squares

We describe the design and computational performance of parallel row-oriented tensor algorithms for the solution of dense systems of nonlinear equations and nonlinear least squares problems on a distributed-memory MIMD multiprocessor. Tensor methods are general purpose methods that base each iteration upon a quadratic model of the nonlinear function, rather than the standard linear model, where the second order term is selected so that the model is hardly more expensive to form, store, or solve than standard models. They have been shown to have substantial advantages in robustness and eeciency on sequential computers. Experimental results obtained on an Intel iPSC2 hypercube show that the tensor method parallelizes virtually as well as a standard method, and that the parallel tensor method obtains nearly full eeciency when the ratio of the number of equations to the number of processors is suuciently large.