On the calculation of orthogonal vectors
Open Access
- 1 January 1968
- journal article
- research article
- Published by Oxford University Press (OUP) in The Computer Journal
- Vol. 11 (3) , 302-304
- https://doi.org/10.1093/comjnl/11.3.302
Abstract
Given an orthonormal basis, d1, d2,..., dn of Euclidean n-space, and given some vector d0 which is not orthogonal to dn, this paper shows how to calculate, in O(n2) computer operations, a new orthonormal basis, d1*, d2*,...,dn*, having the property that dk* is a linear combination of the k vectors d0, d1,...,dk−1. The method is useful because it reduces the amount of computer time that is needed by Rosenbrock's (1960) minimisation procedure. We show that any errors do not grow if the method is applied many times.Keywords
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