Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2005-02-22
2005-02-22
Mai, Tan V (Department: 2124)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
C708S520000
Reexamination Certificate
active
06859817
ABSTRACT:
A computer-based system for solving a system of nonlinear equations specified by a vector function, f, wherein f(x)=0 represents ƒ1(x)=0, ƒ2(x)=0, ƒ3(x)=0, . . . , ƒn(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 Xiincludes 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 ƒi(x)=0 in the system of equations f(x)=0, each individual component function ƒi(x) can be written in the form ƒi(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′jcan be obtained: x′j=g−1(h(x)). Next, the system substitutes the interval vector element Xjinto 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′jwith Xjand replaces Xjin 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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Hansen Eldon R.
Walster G. William
Mai Tan V
Park Vaughan & Fleming LLP
Sun Microsystems Inc.
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