Roundoff-Error-Free Basis Updates of LU Factorizations for the Efficient Validation of Optimality Certificates

2017 ◽  
Vol 38 (3) ◽  
pp. 829-853 ◽  
Author(s):  
Adolfo R. Escobedo ◽  
Erick Moreno-Centeno
Keyword(s):  
Roundoff Error ◽  
Free Basis

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

Roundoff Error in Computing Derivatives Using the Chebyshev Differentiation Matrix

1995 ◽  
Vol 116 (2) ◽  
pp. 380-383 ◽  
Author(s):  
Alvin Bayliss ◽  
Andreas Class ◽  
Bernard J. Matkowsky
Keyword(s):  
Roundoff Error ◽  
Differentiation Matrix ◽  
Chebyshev Differentiation Matrix
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