Recursive Polynomial Remainder Sequence and the Nested Subresultants

TL;DR

This paper introduces two new expressions for subresultants in recursive polynomial remainder sequences, with the reduced nested subresultant significantly decreasing matrix size, enhancing computational efficiency and applicability in approximate algebraic computation.

Contribution

The paper presents the reduced nested subresultant, a novel expression that simplifies recursive PRS analysis and improves computational efficiency over previous methods.

Findings

Reduced nested subresultant drastically decreases matrix size.

Enhanced efficiency in recursive polynomial remainder sequence computations.

Potential applications in approximate algebraic computation.

Abstract

We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced by the author. The reduced nested subresultant reduces the size of the subresultant matrix drastically compared with the recursive subresultant proposed by the authors before, hence it is much more useful for investigation of the recursive PRS. Finally, we discuss usage of the reduced nested subresultant in approximate algebraic computation, which motivates the present work.