On Round-Off Errors in Linear Programming

✍ Scribed by H. Müller-Merbach (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1970
• Tongue: English
• Leaves: 54
• Series: Lecture Notes in Operations Research and Mathematical Systems 37
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-V
Introduction....Pages 1-2
The Examples....Pages 3-6
The Programs....Pages 7-10
The Increase and Cumulation of Round-Off Errors....Pages 11-13
The Use of Easily Computed Checks as a Trigger for Error Elimination....Pages 14-16
The Zero-Check for Eliminating Non-Significant Elements....Pages 17-25
“Ill-Conditioned” Vertices....Pages 26-29
Some General Remarks....Pages 30-33
Acknowledgment....Pages 34-34
Back Matter....Pages 35-50

✦ Subjects

Operations Research/Decision Theory; Economic Theory