On strata of degenerate polyhedral cones, II: Relations between condition measures

Authors:
Dennis Cheung;Felipe Cucker;Javier Peña
Affiliations:
United International College, Tang Jia Wan, Zhuhai, Guandong Province, PR China;Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890, USA
Venue:
Journal of Complexity
Year:
2010

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Abstract

In a paper Cheung, Cucker and Pena (in press) [5] that can be seen as the first part of this one, we extended the well-known condition numbers for polyhedral conic systems C(A) Renegar (1994, 1995) [7-9] and C(A) Cheung and Cucker (2001) [3] to versions C@?(A) and C@?(A) that are finite for all input matrices A@?R^n^x^m. In this paper we compare C@?(A) and C@?(A) with other condition measures for the same problem that are also always finite.