A Symbolic Approach to Compute a Null-Space Basis in the Projection Method

Mark Giesbrecht () and Nam Pham ()
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Mark Giesbrecht: University of Waterloo, Cheriton School of Computer Science
Nam Pham: University of Waterloo, Cheriton School of Computer Science

A chapter in Computer Mathematics, 2014, pp 243-259 from Springer

Abstract: Abstract We present a hybrid symbolic-numeric approach for the so-called projection method for solving the parameterized differential-algebraic constraint equations associated with multibody mechanical systems. A primary problem in this approach is computing a null-space basis of a matrix of multivariate rational functions, the Jacobian of the symbolic constraint matrix. A purely symbolic approach is untenable in terms of the sheer size of the output, whereas a purely numerical approach does not offer the flexibility of leaving some or all parameters unspecified. Instead we propose a hybrid approach, which does a symbolic preconditioning, followed by representing the null-space basis by straight-line C code, i.e., a black-box null-space basis. We do this in a numerically sensitive way, and show that our black box is numerically robust at almost all parameter settings. This is verified by experimental results on inputs from typical multibody models.

Keywords: Singular Value Decomposition; Multibody System; Gaussian Elimination; Permutation Matrice; Random Evaluation (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-43799-5_19

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DOI: 10.1007/978-3-662-43799-5_19

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