Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

In this paper, we develop two piecewise polynomial methods for the numerical evaluation of Cauchy Principal Value integrals of oscillatory kind. The two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. Two numerical examples are presented to illustrate the two rules developed, The convergence of the two schemes is proved and some error bounds obtai...

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...