| 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 f(x)=0, as well as a representation of an initial interval, X, wherein this representation of X 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. Next, the system symbolically manipulates the nonlinear equation f(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 f(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.
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