Solving a nonlinear equation through interval arithmetic and term consistency

摘要

One embodiment of the present invention provides a system for solving a nonlinear equation through interval arithmetic. During operation, the system receives a representation of the nonlinear equation ƒ(x)=0, as well as a representation of an initial interval, X, wherein this representation of X includes a first floating-point number, X_L, for the left endpoint of X, and a second floating-point number, X_U, for the right endpoint of X. Next, the system symbolically manipulates the nonlinear equation ƒ(x)=0 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 g₁^−1(x). The system then plugs the initial interval X into the modified equation to produce the equation g₁(X′)=h₁(X), and solves for X′=g₁^−1[h₁(X)]. Next, the system intersects X′ with the initial interval X to produce a new interval X^+, wherein the new interval X^+ contains all solutions of the equation ƒ(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.