On the Explicit Determination of the Polar Decomposition in n-Dimensional Vector Spaces
- C.S. Jog
- … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.
- P.G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity. North-Holland, Amsterdam (1988).
- L.P. Franca, An algorithm to compute the square root of a 3× 3 positive definite matrix. Comput. Math. Appl. 18 (1989) 459–466.
- I. Gohberg and V. Olshevsky, The fast generalized Parker-Traub algorithm for inversion of Vandermonde and related matrices. J. Complexity 13(2) (1997) 208–234.
- D. Guan-Suo, Determination of the rotation tensor in the polar decomposition. J. Elasticity 50(3) (1998) 197–207.
- M.E. Gurtin, An Introduction to Continuum Mechanics. Academic Press, New York (1984).
- A. Hoger, and D.E. Carlson, Determination of the stretch and rotation in the polar decomposition of the deformation gradient. Quart. Appl. Math. 42 (1984) 113–117.
- J.E. Marsden and T.J.R. Hughes, Mathematical Foundations of Elasticity. Prentice-Hall, Englewood Cliffs, NJ (1983).
- L. Rosati, Derivatives and rates of the stretch and rotation tensors. J. Elasticity 56(3) (1999) 213–230.
- T.C.T. Ting, Determination of C 1/2, C-1/2 and more general isotropic tensor functions of C. J. Elasticity 15 (1985) 319–323.
- S. Wolfram, The Mathematica Book. Cambridge Univ. Press, Cambridge (1996).
- P. Zielinski and K. Zietak, The polar decomposition-properties, applications and algorithms. Appl. Math. 38 (1995) 24–49.
- On the Explicit Determination of the Polar Decomposition in n-Dimensional Vector Spaces
Journal of elasticity and the physical science of solids
Volume 66, Issue 2 , pp 159-169
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- polar decomposition
- square roots of tensors
- explicit determination
- Industry Sectors
- C.S. Jog (1)
- Author Affiliations
- 1. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India