Patent ID: 6859817

Claim:
A method for using a computer system to solve a system of nonlinear equations specified by a vector function, f, wherein f(x)=0 represents ƒ 1 (x)=0, ƒ 2 (x)=0, ƒ 3 (x)=0, . . . , ƒ n (x)=0, wherein x is a vector (x 1 , x 2 , x 3 , . . . x n ), the method comprising: receiving a representation of an interval vector X=(X 1 , X 2 , . . . , X n ), wherein for each dimension, i, the representation of X i , includes a first floating-point number, a i , representing the left endpoint of X i , and a second floating-point number, b i , representing the right endpoint of X i ; for each nonlinear equation ƒ i (x)=g(x′ j )−h(x)=0 in the system of equations f(x)=0, symbolically manipulating ƒ i (x)=0 within the computer system to solve for any invertible term, g(x′ j ), thereby producing a modified equation g(x′ j )=h(x), wherein g(x′ j ) is analytically inverted to produce an inverse function g −1 (y); substituting the interval vector X into the modified equation to produce the equation g(X′ j )=h(X); solving for X′ j =g −1 (h(X)); and intersecting X′ j with the vector element X j to produce a new interval vector X + ; wherein the new interval vector X + contains all solutions of the system of equations f(x)=0 within the interval vector X, and wherein the width of the new interval vector X + is less than or equal to the width of the interval vector X.