Patent ID: 7296047

Claim:
A computer-readable storage device storing instructions that when executed by a computer cause the computer to perform a method for solving an overdetermined system of interval linear equations within a computer system, wherein the computer-readable storage device does not include computer instruction signals embodied in a transmission medium, and wherein the method comprises: receiving a representation of the overdetermined system of interval linear equations Ax=b, wherein A is a matrix with m rows corresponding to m equations, and n columns corresponding to n variables, wherein x includes n variable components, b includes m scalar components, and m>n; storing the representation in a memory within the computer system; performing a Gaussian Elimination operation to transform Ax=b into the form [ T W ] ⁢ x = [ u v ] , thereby facilitating arithmetic operations in the computer; wherein T is a square upper triangular matrix of order n, u is an interval vector with n components, v is an interval vector with m−n components, and W is a matrix with m−n rows and n columns; wherein W is zero except in the last column, which is represented as a column vector z with m−n components; performing an interval intersection operation based on the equations z i x n =v i (i=1, . . . , m−n) and T nn x n =u n to solve for x n = u n ⁢ T nn ⁢ ⋂ i = 1 m - n ⁢ v i z i , which are bounds for an unknown solution of x n ; if x n is not the empty interval, performing a back substitution operation using x n and Tx=u to solve for the remaining components (x n−1 , . . . , x 1 ) of x; using the components of x to determine the accuracy of a computation performed in an arithmetic unit.