Half-GCD and fast rational recovery

Over the past few decades several variations on a “half GCD” algorithm for obtaining the pair of terms in the middle of a Euclidean sequence have been proposed. In the integer case algorithm design and proof of correctness are complicated by the effect of carries. This paper will demonstrate a variant with a relatively simple proof of correctness. We then apply this to the task of rational recovery for a linear algebra solver. Categories and Subject Descriptors F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems—Number

• Type: Conference
• Year: 2005
• Where: ISSAC
• Authors: Daniel Lichtblau
• Keywords: Algorithms, Case Algorithm Design, Half Gcd, ISSAC 2005