Patent ID: 7222145

Claim:
A method for using a computer system to solve a system of equations in fixed-point form, comprising: receiving a source code for performing interval calculations; compiling the source code into an executable code; receiving the system of equations in fixed-point form, wherein the system of equations is specified using intervals, wherein the intervals bound measurement errors and machine-rounding errors; storing the system of equations in a computer memory; and executing the executable code to: reduce the dimension of the system of equations, when possible, by eliminating variables in the system of equations to produce a reduced system of equations thereby reducing the computation time required by the computer system to solve the system of equations, perform interval intersections based on the Fixed Point theorem to reduce the size of a box containing solutions to the reduced system of equations thereby reducing the size of the computer memory required to store the system of equations, and to apply interval techniques to find solutions to the system of equations, when such solutions exist, wherein the interval techniques are performed by a hardware interval computation unit, and wherein the solutions to the system of equations include bounding of measurement errors and machine-rounding errors.