Matrices with Bidiagonal Decomposition, Accurate Computations and Corner Cutting Algorithms

Abstract

Some important classes of matrices admit a factorization known as bidiagonal decomposition. Bidiagonal decompositions can provide natural parameters to perform computations with high relative accuracy. We prove that corner cutting algorithms provide bidiagonal decompositions with high relative accuracyKeywordsBidiagonal decompositiontotally positive matriceshigh relative accuracycorner cutting algorithm.