POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION

Resumo

Existing methods for quadratic forms classification have exponential time complexity or use approximation that weaken the result reliability. We develop an algorithm that improves the best case of quadratic form classification in constant time and is polynomial in the worst case. In addition, new strategies were used to guarantee the results reliability, by representing rational numbers as a fraction of integers and to identify linear combinations that are linearly independent using Gaussian Elimination.

DOI: 10.36558/rsc.v11i3.7391