An iterative scheme for testing the positive definiteness of multivariate homogeneous forms*. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Zhang, Kaili; Zhang, Haibin; Zhao, Pengfei; Wang, Xueyong
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 12(2019)
• Page Start: 2461
• Page End: 2472
• Publication Date: 2019-12-02
• Subjects: Positive definiteness -- strong H-tensor -- homogeneous multivariate form -- weakly reducible -- iterative scheme; 15A18 -- 15A69 -- 12E05 -- 65F10; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1567915
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: A positive-definite homogeneous multivariate form plays a critical role in the medical imaging and automatic control, and the definiteness of this form can be identified by a special structure tensor. In this paper, we first state the equivalence between the positive-definite multivariate form and the corresponding tensor and account for the links between the positive-definite tensor with a strong H -tensor. Then based on weak reducibility, some criteria were provided to identify strong H -tensors. Furthermore, with these relations, we establish an iterative scheme to identify the positive-definite multivariate homogeneous form and prove it is theoretically valid. Numerical experiments were given to illustrate the practicality of the scheme.