Müller-Merbach On Round-Off Errors in Linear Programming

Erscheinungsjahr 2012
ISBN: 978-3-642-95167-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 37, 50 Seiten, eBook

Reihe: Lecture Notes in Economics and Mathematical Systems

Due to the limited number of digits or bits per storage location in electronic computers, round-off errors arise during arithmetic operations. Depending upon the kind of operation, the structure of the data, and the skillfulness of the program, these errors increase and spread out more or less quickly during a continued computation process in which the computed data affected by errors are themselves used for generating new data. The purpose of this investigation was to learn about the increase of round-off errors in linear programming procedures. Less attention was paid to the theory of round-off errors or to the effectiveness of error elimination procedures. In regard to these questions the results of in vestigations which have been made on round-off errors in a more general context dealing with matrix inversion and eigenvalue problems could be used for the purposes of this paper. The emphasis of this investigation lay rather on studying the behavior of typical linear programming problems from the pOint of view of error cumulation.

Zielgruppe

Research

Autoren/Hrsg.

Müller-Merbach, H.

Inhaltsverzeichnis

I. Introduction.- II. The Examples.- III. The Programs.- IV. The Increase and Cumulation of Round-Off Errors.- V. The Use of Easily Computed Checks as a Trigger for Error Elimination.- VI. The Zero-Check for Eliminating Non-Significant Elements.- VII. “Ill-Conditioned” Vertices.- VIII. Some General Remarks.- IX. Acknowledgment.- References.