Term Cancellations in Computing Floating-Point Grobner Bases

摘要

We discuss the term cancellation which makes the floatingpoint Grobner basis computation unstable, and show that error accumulation is never negligible in our previous method. Then, we present a new method, which removes accumulated errors as far as possible by reducing matrices constructed from coefficient vectors by the Gaussian elimination. The method manifests amounts of term cancellations caused by the existence of approximate linearly dependent relations among input polynomials.