Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (2)

Search Parameters:
Keywords = B-biquadratic tensors

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
26 pages, 487 KiB  
Article
Biquadratic Tensors: Eigenvalues and Structured Tensors
by Liqun Qi and Chunfeng Cui
Symmetry 2025, 17(7), 1158; https://doi.org/10.3390/sym17071158 - 20 Jul 2025
Cited by 1 | Viewed by 205
Abstract
The covariance tensors in statistics and Riemann curvature tensor in relativity theory are both biquadratic tensors that are weakly symmetric, but not symmetric in general. Motivated by this, in this paper, we consider nonsymmetric biquadratic tensors and extend M-eigenvalues to nonsymmetric biquadratic tensors [...] Read more.
The covariance tensors in statistics and Riemann curvature tensor in relativity theory are both biquadratic tensors that are weakly symmetric, but not symmetric in general. Motivated by this, in this paper, we consider nonsymmetric biquadratic tensors and extend M-eigenvalues to nonsymmetric biquadratic tensors by symmetrizing these tensors. We present a Gershgorin-type theorem for biquadratic tensors, and show that (strictly) diagonally dominated biquadratic tensors are positive semi-definite (definite). We introduce Z-biquadratic tensors, M-biquadratic tensors, strong M-biquadratic tensors, B0-biquadratic tensors, and B-biquadratic tensors. We show that M-biquadratic tensors and symmetric B0-biquadratic tensors are positive semi-definite, and that strong M-biquadratic tensors and symmetric B-biquadratic tensors are positive definite. A Riemannian Limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method for computing the smallest M-eigenvalue of a general biquadratic tensor is presented. Numerical results are reported. Full article
(This article belongs to the Section Mathematics)
Show Figures

Figure 1

17 pages, 2522 KiB  
Article
Quadratic B-Spline Surfaces with Free Parameters for the Interpolation of Curve Networks
by Paola Lamberti and Sara Remogna
Mathematics 2022, 10(4), 543; https://doi.org/10.3390/math10040543 - 10 Feb 2022
Cited by 1 | Viewed by 3130
Abstract
In this paper, we propose a method for constructing spline surfaces interpolating a B-spline curve network, allowing the presence of free parameters, in order to model the interpolating surface. We provide a constructive algorithm for its generation in the case of biquadratic tensor [...] Read more.
In this paper, we propose a method for constructing spline surfaces interpolating a B-spline curve network, allowing the presence of free parameters, in order to model the interpolating surface. We provide a constructive algorithm for its generation in the case of biquadratic tensor product B-spline surfaces and bivariate B-spline surfaces on criss-cross triangulations. Finally, we present graphical results. Full article
(This article belongs to the Special Issue Spline Functions and Applications)
Show Figures

Figure 1

Back to TopTop