Determining the equivalence of two sets of simultaneous...

Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed

Reexamination Certificate

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C708S160000

Reexamination Certificate

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07836112

ABSTRACT:
A computer implemented method (200) is described for determining the equivalence of two sets of simultaneous linear algebraic equations. Each of said equations is of a form:in-line-formulae description="In-line Formulae" end="lead"?ei1x1+ei2x2+ei3x3+ . . . +eiixn=biin-line-formulae description="In-line Formulae" end="tail"?wherein xjare unknowns, eijare coefficients and biare quantities, and defining the relationship between the unknowns within the set. The coefficients and quantities are known algebraic expressions. The unknowns are iteratively eliminated (250to280) from each of the sets of simultaneous linear algebraic equations until each of said equations are in the form:in-line-formulae description="In-line Formulae" end="lead"?(lii)kxi=(ri)kin-line-formulae description="In-line Formulae" end="tail"?wherein liiand riare algebraic expressions, and k={1;2} indicate one of said sets that said equation is derived from. The products (lii)1*(ri)2and (lii)2*(ri)1are compared (300) for each of the unknowns. Only if the products match (310) for all the unknowns are the two sets of simultaneous linear algebraic equations equivalent (312). An apparatus (100) for performing the above method (200) is also provided.

REFERENCES:
patent: 5200915 (1993-04-01), Hayami et al.
patent: 5343554 (1994-08-01), Koza et al.
patent: 5392429 (1995-02-01), Agrawal et al.
patent: 6601080 (2003-07-01), Garg
patent: 2002/0007385 (2002-01-01), Stoutemyer
Anthony Ralston, “A First Course in Numerical Analysis”, 1965, McGraw-Hill Inc, pp. 394-463.

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