Patent ID: 6993548

Claim:
A method for bounding the solution set of a system of linear equations Ax=b, wherein A is an interval matrix and b is an interval vector, the method comprising: receiving the system of linear equations Ax=b; storing Ax=b in a memory in a computer system; preconditioning the set of linear equations Ax=b by multiplying both side of the linear equations by a matrix B to produce a preconditioned set of linear equations BAx=Bb, wherein the set of linear equations is a representation of a global optimization problem; substituting M 0 =BA and r=Bb to produce M 0 x=r; widening the matrix M 0 to produce a widened matrix M, wherein the midpoints of the interval elements of M form the identity matrix; and using M and r to compute a hull h of the system Mx=r, which bounds the solution set of the system M 0 x=r; wherein the interval operations involved in bounding the solution set are performed using a special-purpose interval arithmetic unit configured to perform interval arithmetic operations.