| 摘要 |
One embodiment of the present invention provides a computer-based system for solving a system of nonlinear equations specified by a vector function, f, wherein f(x)=0 represents f<SUB>1</SUB>(x)=0, f<SUB>2</SUB>(x)=0, f<SUB>3</SUB>(x)=0 . . . , f<SUB>n</SUB>(x)=0, wherein x is a vector (x<SUB>1</SUB>, X<SUB>2</SUB>, X<SUB>3</SUB>, . . . x<SUB>n</SUB>). The system operates by receiving a representation of a subbox X=(X<SUB>1</SUB>, X<SUB>2</SUB>, . . . , X<SUB>n</SUB>), wherein for each dimension, i, the representation of X<SUB>i</SUB>, includes a first floating-point number, a<SUB>i</SUB>, representing the left endpoint of X<SUB>i</SUB>, and a second floating-point number, b<SUB>i</SUB>, representing the right endpoint of X<SUB>i</SUB>. The system stores the representation in a computer memory. Next, the system applies term consistency to the set of nonlinear equations, f<SUB>1</SUB>(x)=0, f<SUB>2</SUB>(x)=0, f<SUB>3</SUB>(x)=0, . . . , f<SUB>n</SUB>,(x)=0, over X, and excludes portions of X that violate the set of nonlinear equations. The system also applies box consistency to the set of nonlinear equations over X, and excludes portions of X that violate the set of nonlinear equations. Finally, the system performs an interval Newton step on X to produce a resulting subbox Y, wherein the point of expansion of the interval Newton step is a point x within X, and wherein performing the interval Newton step involves evaluating f(x) using interval arithmetic to produce an interval result f<SUP>I</SUP>(x). The system integrates the sub-parts of the process with branch tests designed to increase the overall speed of the process.
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