Solving Nonlinear Systems on a Vector Supercomputer * Chenyi Hu, Baker Kearfott, Joe Sheldon and Qing Yang Abstract Interval Newton methods in conjunction with generalized bisection form the basis of algorithms that find all real roots within a specified X ⊂ R n of a system of nonlinear equa- tions F (X )=0 with mathematical certainty, even in finite-precision arithmetic. INTBIS [4] is a well-tested software package which finds all numerical solutions for nonlinear systems of equations globally by using interval Newton/generalized bisection method on a single processor computer system. Since interval computations are used in INTBIS, the rigor of numerical results is guaranteed. However, the algorithm is still computationally costly. This paper proposes parallel implementations of the INTBIS on a vector supercomputer: Cray Y-MP. Two implementations have been tested that take into account the architec- tural features of the vector computer. Our measurements show that the implementations are very efficient. 1 Introduction: Solving nonlinear systems of equations is of fundamental importance in a large class of scientific and engineering applications. While the classic Newton method is robust in solving nonlinear systems, it does not mathematically guarantee to find all roots of a nonlinear system of equations within a given domain. Since we only perform finite-precision arithmetics on a computer, a result obtained by a traditional scalar operations may not be reliable mathematically or computation ally. INTBIS [4] is a software package (in FORTRAN 77) that solves large nonlinear systems of equations using preconditioned interval Newton method in conjunction with generalized bi- section. It utilizes the new preconditioned scheme called all-row preconditioned scheme which has the advanteges of lower computational complexity and fast convergence rate. The INTBIS guarantees to find all real roots within the specified domain of a nonlinear system with both mathematical and computational certainty. * This research was partially supported by NSF Grant No. DMS-9205680 and No. MIP-9208041. 1