Patent ID: 6823352
Filing Date: 2004-11-23
Classification: G06F

Abstract:
A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for using a computer system to solve a nonlinear equation by using interval arithmetic, the method comprising:receiving a representation of the nonlinear equation Æ’(x)=0 within the computer system; receiving a representation of an initial interval, X, within the computer system, wherein the representation includes a first floating-point number, XL, for the left endpoint of X, and a second floating-point number, XU, for the right endpoint of X; symbolically manipulating the nonlinear equation Æ’(x)=0 within the computer system to solve for a first term, g1(x), thereby producing a modified equation g1(x)=h1(x), wherein the first term g1(x) can be analytically inverted to produce an inverse function g1âˆ’1(x); plugging the initial interval X into the modified equation to produce the equation g1(Xâ€²)=h1(X); solving for Xâ€²=g1âˆ’1[h1(X)]; and intersecting Xâ€² with the initial interval X to produce a new interval X+; wherein the new interval X+ contains all solutions of the equation Æ’(x)=0 within the initial interval X, and wherein the size of the new interval X+ is less than or equal to the size of the initial interval X.