Computation of the exponential and other isotropic tensor functions and their derivatives

✍ Scribed by Mikhail Itskov

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 169 KB
• Volume: 192
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(03)00397-9

✦ Synopsis

In the present paper we focus on numerical aspects of the computation of isotropic tensor functions and their derivative. In the general case of non-symmetric tensor arguments only two numerical algorithms appear to be appropriate. The first one represents a recurrent procedure resulting from the Taylor power series expansion of an isotropic tensor function. The second algorithm is based on a recently proposed closed-form representation which can be obtained from the definition of an isotropic tensor function either by the tensor power series or by the Dunford-Taylor integral. To improve the accuracy in the case of nearly equal eigenvalues a series expansion of this closed formula is proposed. Both algorithms are finally illustrated by an example of the exponential tensor function where emphasis is placed on the precision issue.