| 摘要 |
A computer-based system for solving a system of nonlinear equations specified by a vector function, f, wherein f(x)=0 represents f1(x)=0, f2(x)=0, f3(x)=0, . . . , fn(x)=0, wherein x is a vector (x1, x2, x3, . . . xn). The system operates by receiving a representation of an interval vector X=(X1, X2, . . . , Xn), wherein for each dimension, i, the representation of Xi includes a first floating-point number, ai, representing the left endpoint of Xi, and a second floating-point number, bi, representing the right endpoint of Xi. For each nonlinear equation fi(x)=0 in the system of equations f(x)=0, each individual component function fi(x) can be written in the form fi(x)=g(x'j)-h(x) or g(x'j)=h(x), where g can be analytically inverted so that an explicit expression for x'j can be obtained: x'j=g<-1>(h(x)). Next, the system substitutes the interval vector element Xj into the modified equation to produce the equation g(X'j)=h(X), and solves for X'j=g<-1>(h(X)). The system then intersects X'j with Xj and replaces Xj in the interval vector X 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.
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