Is the precision of computed solutions more closely related with componentwise condition number than normwise condition number?

Abstract

We have a conjecture that “the precision of computed solutions for systems of linear equations is more closely related with componentwise condition number c(A) than normwise condition number κ(A). We conducted simulation experiments to verify this conjecture. A statistical tool, Hotelling-Williams T-Test is employed to check if difference between correlations is significant. Simulation results suggest that our conjecture is true for most of the well-known methods and matrix sizes. Keywords: condition numbers, simulation, correlation coefficients, Hotelling-Williams T-Test

Date of Award	1 May 2015
Original language	English
Supervisor	Chin Wing Dennis Cheung (Supervisor)