Patent ID: 6920472

Claim:
A method for using a computer system to find the roots of a system of nonlinear equations within an interval vector X, wherein the system of non-linear equations is specified by a vector function, ƒ, the method comprising: receiving a representation of the interval vector X, wherein for each dimension, i, the representation of X i includes a first floating-point number, α i , representing the left endpoint of X i , and a second floating-point number, b i , representing the right endpoint of X i ; storing the representation in a memory of the computer system; performing an interval Newton step on X to produce a resulting interval vector, X′, wherein the point of expansion of the interval Newton step is a point, x, within the interval X, and wherein performing the interval Newton step involves evaluating ƒ(x) to produce an interval result ƒ 1 (x); evaluating a first termination condition, wherein the first termination condition is TRUE if, zero is contained within ƒ 1 (x), J(x,X) is regular, wherein J(x,X) is the Jacobian of the function ƒ evaluated with respect to x over the interval X, and X is contained within X′; and if the first termination condition is TRUE, terminating the interval Newton method and recording X′ in the memory as a final bound.