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2012 | OriginalPaper | Chapter

Numerical Root Finding from an Engineer’s Point of View

Authors : M. Färber, U. Döring

Published in: Mechanisms, Transmissions and Applications

Publisher: Springer Netherlands

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Abstract

The article starts with a presentation of a straight-forward global root finding algorithm featuring Newton-Raphson-like local root finding to find all solutions. After an analysis of the causes why it may fail, strategies are given to improve root finding. The strategies are tested and statistically analyzed with respect to two practical mechanical engineering problems: determining the point positions of an Assur group of third order and determining the translation and orientation of a Stewart Gough platform. In conclusion, ten advices are given on how to do root finding successfully and quickly.

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Literature
1.
Bonnans, J. F., Gilbert, J. C., Lemaréchal, C., Sagastizábal, C. A.: Numerical Optimization. Theoretical and Practical Aspects. 2nd ed., Springer, Berlin, 2006.MATH
2.
Broyden, C. G.: A class of methods for solving nonlinear simultaneous equations. Mathematics of Computation, 19(92), 577-593 (1965).MathSciNetMATHCrossRef
3.
Buchberger, B., Winkler, F. (eds): Gröbner Bases and Applications. Cambridge University Press, Cambridge, MA, 2000.
4.
Deuflhard, P.: Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms. Springer, Berlin, 2004.MATH
5.
Döring, U.: Ficucs - Ein Constraint-Solver für geometrische Constraints in 2D und 3D. PhD thesis, Ilmenau University of Technology, Ilmenau, Germany, 2011.
6.
Engeln-Müllges, G., Uhlig, F: Numerical Algorithms with C. Springer, Berlin, 1996.MATH
7.
M. Färber, B. Brüderlin: Multivariate root finding with search space decomposition and randomisation. in: Proceedings of the Symposium on Applied Computing (SAC’09), Honululu, HI, pp. 1142-1143 (2009).
8.
Hubbard, J. H., Schleicher, D., Sutherland, S.: How to find all roots of complex polynomials by Newton’s method. Inventiones Mathematicae, 146(1), 1-33 (2001).MathSciNetMATHCrossRef
9.
Kantorowitsch, L. W., Akilow, G. P.: Funktionalanalysis in normierten Räumen. 2nd ed., Akademie-Verlag, Berlin, 1978.
10.
11.
Miranda, C.: Un’osservazione su un teorema di Brouwer. Bollettino dell’Unione Matematica Italiana, II. Serie, 3, 5-7 (1940).MathSciNetMATH
12.
Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T.: Numerical Recipes in C: The Art of Scientific Computing. 2nd ed., Cambridge University Press, Cambridge, MA, 1992.
13.
Ritt, J. F.: Differential Algebra. Dover Publications, New York, NY, 1950.MATH
14.
Shoemake, K.: Quaternions and 4 x 4 Matrices. In: Arvo, J. (ed.): Computer Graphics Gems II. Academic Press, San Diego, CA, 1991.
15.
Stewart, D.: A platform with six degrees of freedom. In: UK Institution of Mechanical Engineers Proceedings, Volume 180, Part 1, Number 15, pp. 371-386 (1965).
16.
Sturmfels, B.: Introduction to resultants. In: Proceedings of Symposia in Applied Mathematics, 53, pp. 25-39 (1997).
17.
Volmer, J. (ed.): Grundlagen Getriebetechnik. Verlag Technik, Berlin, 1992.
Metadata
Title
Numerical Root Finding from an Engineer’s Point of View
Authors
M. Färber
U. Döring
Copyright Year
2012
Publisher
Springer Netherlands
Book
Mechanisms, Transmissions and Applications

Print ISBN: 978-94-007-2726-7

Electronic ISBN: 978-94-007-2727-4

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-94-007-2727-4_8

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