In this paper we propose a new fast O(n) algorithm for solving Cauchy linear systems of equations. An a priori rounding error analysis, which provides bounds for the forward, backward and residual errors associated with the computed solution, indicates that for the class of totally positive Cauchy matrices the proposed algorithm is forward and backward stable, producing a remarkably high relati...

Small-distortion constitutive laws are often extemporaneously generalized to large deformations by merely applying them in the unrotated material frame or, equivalently, by using polar rates. This approach does render the resulting constitutive model indifferent to large superimposed rigid rotations, but it may lead to incorrect predictions for both the magnitude and direction of stress wheneve...