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Karle-Hauptman Matrices and Eigenvalues: a Practical Approach

Karle-Hauptman Matrices and Eigenvalues: a Practical Approach The possible usefulness of eigenvectors and eigenvalues of Karle-Hauptman matrices is examined. The eigenvalue spectra of structures with calculated and measured 's are discussed and the result of several attempts at phase refinement are reported. The use of the sum of the square of the negative eigenvalues (SSNE) as a goodness-of-fit criterion is examined. The possible use of a priori information is investigated using the approximation of orthogonal electron densities corresponding to eigenvectors with eigenvalues greater than zero. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A: Foundations of Crystallography International Union of Crystallography

Karle-Hauptman Matrices and Eigenvalues: a Practical Approach

Karle-Hauptman Matrices and Eigenvalues: a Practical Approach


Abstract

The possible usefulness of eigenvectors and eigenvalues of Karle-Hauptman matrices is examined. The eigenvalue spectra of structures with calculated and measured 's are discussed and the result of several attempts at phase refinement are reported. The use of the sum of the square of the negative eigenvalues (SSNE) as a goodness-of-fit criterion is examined. The possible use of a priori information is investigated using the approximation of orthogonal electron densities corresponding to eigenvectors with eigenvalues greater than zero.

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Publisher
International Union of Crystallography
Copyright
Copyright (c) 1998 International Union of Crystallography
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/S0108767397013603
Publisher site
See Article on Publisher Site

Abstract

The possible usefulness of eigenvectors and eigenvalues of Karle-Hauptman matrices is examined. The eigenvalue spectra of structures with calculated and measured 's are discussed and the result of several attempts at phase refinement are reported. The use of the sum of the square of the negative eigenvalues (SSNE) as a goodness-of-fit criterion is examined. The possible use of a priori information is investigated using the approximation of orthogonal electron densities corresponding to eigenvectors with eigenvalues greater than zero.

Journal

Acta Crystallographica Section A: Foundations of CrystallographyInternational Union of Crystallography

Published: May 1, 1998

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