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1969•IMA Journal of Applied MathematicsRequires access

A Technique for Orthogonalization

Roger Fletcher

Open publisher page 18 citations

Abstract

An alternative to the Gram—Schmidt process is deseribed for carrying out orthogonalization of a given vector with respect to a given set of vectors. The technique is especially advantageous for problems in which the number of vectors in the set is likely to be both increased and decreased. A generalization to orthogonality with respect to a symmetric positive definite matrix is also deseribed.

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What this paper is about

An alternative to the Gram—Schmidt process is deseribed for carrying out orthogonalization of a given vector with respect to a given set of vectors. The technique is especially advantageous for problems in which the number of vectors in the set is likely to be both increased and decreased. A generalization to orthogonality with respect to a symmetric positive definite matrix is also deseribed.

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OpenAlex reports 18 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

An alternative to the Gram—Schmidt process is deseribed for carrying out orthogonalization of a given vector with respect to a given set of vectors. The technique is especially advantageous for problems in which the number of vectors in the set is likely to be both increased and decreased. A generalization to orthogonality with respect to a symmetric positive definite matrix is also deseribed.

Key concepts: Orthogonalization, Orthogonality, Generalization, Mathematics, Set (abstract data type), Matrix (chemical analysis), Applied mathematics, Combinatorics

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