Gregory J. Ward

Opposite-Side Residuals in Working-Precision Newton-Schulz Refinement of LU-Based Matrix Inverses: Measurements and an Empirical Predictor

An inverse X of a matrix A computed through an LU factorization comes with a guarantee on only one of its two residuals, I - AX or I - XA, according to whether it was obtained by solving AX = I or XA = I. In practice the two are usually of the same size, as Wilkinson observed. A...

A Refuted Golden-Ratio Floating-Point Conjecture, Exactly Reversible Integer Maps, and a Fixed-Width Lifting Wavelet

This is an expository paper with a negative result at its centre. It began from a geometric picture of reversible computation, a state that expands by the golden ratio φ = (1+√5)/2 and folds back by 1/φ, and from the conjecture that scaling by φ gives better round-trip accuracy i...