6 papers
Direct Sum and Direct Product Decompositions of Multivariate Functions
Hua-Lin Huang, Yiming Liu, Jianhua Xiang +1
This paper addresses the problem of whether or not a vector-valued multivariate functions can be expressed as a sum or a product of vector-valued functions in disjoint sets of vari…
Qi's problems on classifications of third- and fourth-order symmetric tensors by eigenvalues
Lishan Fang, Hua-Lin Huang
This paper addresses two fundamental problems posed by Qi regarding the sufficiency of eigenvalues for the classification of symmetric tensors in the two-dimensional setting. For $…
Simultaneous block diagonalization of a set of symmetric matrices via congruence
Lishan Fang, Hua-Lin Huang, Jiayan Huang
This article studies canonical forms derived from the finest simultaneous block diagonalization of a set of symmetric matrices via congruence. Our technique relies on Harrison's ce…
Eigenvalues and equivalence classes of third-order symmetric tensors
Lishan Fang, Hua-Lin Huang, Shengyuan Ruan +1
This paper demonstrates that third-order real symmetric tensors cannot be classified up to equivalence by their eigenvalues only, thereby resolving a problem posed by Qi in 2006. B…
Simultaneous direct sum decompositions of several multivariate polynomials
Lishan Fang, Hua-Lin Huang, Lili Liao
We consider the problem of simultaneous direct sum decomposition of a set of multivariate polynomials. To this end, we extend Harrison's center theory for a single homogeneous poly…
Numerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials
Lishan Fang, Hua-Lin Huang, Yuechen Li
We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear form…