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131 results on '"Witzgall, Christoph"'

8. A Purely Algebraic Justification of the Kabsch-Umeyama Algorithm

Author

Lawrence, Jim, Bernal, Javier, and Witzgall, Christoph

Subjects
Mathematics - Optimization and Control
Abstract

The constrained orthogonal Procrustes problem is the least-squares problem that calls for a rotation matrix that optimally aligns two matrices of the same order. Over past decades, the algorithm of choice for solving this problem has been the Kabsch-Umeyama algorithm, which is effectively no more than the computation of the singular value decomposition of a particular matrix. Its justification, as presented separately by Kabsch and Umeyama, is not totally algebraic since it is based on solving the minimization problem via Lagrange multipliers. In order to provide a more transparent alternative, it is the main purpose of this paper to present a purely algebraic justification of the algorithm through the exclusive use of simple concepts from linear algebra. For the sake of completeness, a proof is also included of the well known and widely used fact that the orientation-preserving rigid motion problem, i.e., the least-squares problem that calls for an orientation-preserving rigid motion that optimally aligns two corresponding sets of points in d-dimensional Euclidean space, reduces to the constrained orthogonal Procrustes problem., Comment: 8 pages

Published
2019
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9. Computational Geometry

Author

Beichl, Isabel M., Bernal, Javier, Witzgall, Christoph, Sullivan, Francis, Gass, Saul I., editor, and Fu, Michael C., editor

Published
2013
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10. Voronoi Constructs

Author

Beichl, Isabel M., Bernal, Javier, Witzgall, Christoph, Sullivan, Francis, Gass, Saul I., editor, and Fu, Michael C., editor

Published
2013
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17. Fitting spheres to range data from 3-D imaging systems

Author

Franaszek, Marek, Cheok, Geraldine S., Saidi, Kamel S., and Witzgall, Christoph

Subjects
Imaging technology, Chaos theory -- Analysis, Imaging systems -- Evaluation, Least squares -- Usage
Published
2009

18. An examination of new paradigms for spline approximations

Author

Witzgall, Christoph, Gilsinn, David E., and McClain, Marjorie A.

Subjects
Approximation theory -- Research, Functional equations -- Research, Functions -- Research
Abstract

1. Introduction Over the last decade the task of representing very large 'point clouds' by meshed surfaces has arisen in many applications. Such point clouds may have been generated from […]

Published
2006

19. Evaluation of aerodynamic drag and torque for external tanks in low Earth Orbit

Author

Stone, William C. and Witzgall, Christoph

Subjects
Orbits -- Research, Torque -- Research
Abstract

Introduction During the intervening 15 years since the first publication of this paper, (1) a great many things have changed in the space business. Of the original introduction that follows, […]

Published
2006

20. Integer representation of decimal numbers for exact computations

Author

Bernal, Javier and Witzgall, Christoph

Subjects
Decimal system -- Research, Algebra, Abstract -- Research
Abstract

1. Introduction Mainstream computers base integer and floating point arithmetic on fixed word lengths. As a consequence, only values with a limited number of significant digits can be represented directly, […]

Published
2006

22. Voronoi constructs

Author

Beichl, Isabel, primary, Bernal, Javier, additional, Witzgall, Christoph, additional, and Sullivan, Francis, additional

Published
2001
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23. Computational geometry

Author

Beichl, Isabel, primary, Bernal, Javier, additional, Witzgall, Christoph, additional, and Sullivan, Francis, additional

Published
2001
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27. Convex Sets

Author

Stoer, Josef, Witzgall, Christoph, Doob, J. L., editor, Grothendieck, A., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, Stoer, Josef, and Witzgall, Christoph

Published
1970
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28. Saddle Point Theorems

Author

Stoer, Josef, Witzgall, Christoph, Doob, J. L., editor, Grothendieck, A., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, Stoer, Josef, and Witzgall, Christoph

Published
1970
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29. Duality Theorems

Author

Stoer, Josef, Witzgall, Christoph, Doob, J. L., editor, Grothendieck, A., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, Stoer, Josef, and Witzgall, Christoph

Published
1970
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30. Convex Polyhedra

Author

Stoer, Josef, Witzgall, Christoph, Doob, J. L., editor, Grothendieck, A., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, Stoer, Josef, and Witzgall, Christoph

Published
1970
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31. Convex Functions

Author

Stoer, Josef, Witzgall, Christoph, Doob, J. L., editor, Grothendieck, A., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, Stoer, Josef, and Witzgall, Christoph

Published
1970
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32. Inequality Systems

Author

Stoer, Josef, Witzgall, Christoph, Doob, J. L., editor, Grothendieck, A., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, Stoer, Josef, and Witzgall, Christoph

Published
1970
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33. Introduction

Author

Stoer, Josef, Witzgall, Christoph, Doob, J. L., editor, Grothendieck, A., editor, Heinz, E., editor, Hirzebruch, F., editor, Hopf, E., editor, Hopf, H., editor, Maak, W., editor, MacLane, S., editor, Magnus, W., editor, Postnikov, M. M., editor, Schmidt, F. K., editor, Scott, D. S., editor, Stein, K., editor, Eckmann, B., editor, van der Waerden, B. L., editor, Stoer, Josef, and Witzgall, Christoph

Published
1970
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40. On One-Row Linear Programs

Author

Witzgall, Christoph, Beckmann, Martin J., editor, Künzi, H. P., editor, Fiacco, Anthony V., editor, and Kortanek, Kenneth O., editor

Published
1980
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46. Schrifttumsschau

Author

Münzner, Hans, Röper, Gerhard, Boehm, Carl, Helbig, Manfred, Witzgall, Christoph, and Härlen, Hasso

Published
1957
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48. Some Complete Calculi for Matrices.

Author

Bayer, Rudolf and Witzgall, Christoph

Subjects
*MATRICES (Mathematics), *MATHEMATICAL programming
Abstract

Investigates how the special structure of matrices can be described and utilized for mathematical programming. Symbol manipulation of matrix expressions; Extension of matrix operators to sequence operators and cumulative operators.

Published
1970
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