On the arithmetic operations and propagation of rounding error in gram-schmidt's process of orthonormalisation in recursive form

Sur, BN (1977) On the arithmetic operations and propagation of rounding error in gram-schmidt's process of orthonormalisation in recursive form. Technical Report. National Aeronautical Laboratory, Bangalore, India.

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Abstract

Gram-Schmidt's process of orthonormalisation can be expressed in two forms. One of them directly orthonormalises and the other one orthogonalises first and then normalises.13; The number of arithmetic operations involved in these two forms is formulated in this report. It is found that one of them requires less number of operations. By taking a 13; speeipic example the following are demonstrated.,numerically13; in this report.13; I} An attempt to generate a large number of orthonormal13; funetions by the above process leads to unreliable numerical13; results due to round-off effect.13; 2) The propagation of error is so severe that even if13; we associate the process with a.method suggested by Davis13; to alleviate this round-off effect the numerical results13; cannot be improved.

Item Type: Monograph (Technical Report)
Uncontrolled Keywords: Gram-schmidt's;Orthonormalisation;Arithmetic operations; Round-off effect;Propagation
Subjects: MATHEMATICAL AND COMPUTER SCIENCES > Mathematical and Computer Scienes(General)
Depositing User: Users 90 not found.
Date Deposited: 03 Nov 2006
Last Modified: 24 May 2010 04:22
URI: http://nal-ir.nal.res.in/id/eprint/3184

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