We introduce a new family of strong linearizations of matrix polynomials—which we call
“block Kronecker pencils”—and perform a backward stability analysis of complete …

While interpretable multiview classification is accomplished by recently developed fully
interpretable Takagi-Sugeno-Kang (TSK) classifier FIMG-TSK along each view, this study …

Companion matrices, especially the Frobenius companion matrices, are used in algorithms
for finding roots of polynomials and are also used to find bounds on eigenvalues of matrices …

Computing roots of scalar polynomials as the eigenvalues of Frobenius companion matrices
using backward stable eigenvalue algorithms is a classical approach. The introduction of …

Minimal bases of rational vector spaces are a well-known and important tool in systems
theory. If minimal bases for two subspaces of rational n-space are displayed as the rows of …

We discuss matrix polynomials expressed in a Bernstein basis, and the associated
polynomial eigenvalue problems. Using Möbius transformations of matrix polynomials, large …

Several matrix norms of the classical Frobenius companion matrices of a monic polynomial
p (z) have been used in the literature to obtain simple lower and upper bounds on the …

When Fiedler published his “A note on Companion matrices” in 2003 on Linear Algebra and
its Applications, he could not have foreseen the significance of this elegant factorization of a …

The class of sparse companion matrices was recently characterized in terms of unit
Hessenberg matrices. We determine which sparse companion matrices have the lowest …

We discuss matrix polynomials expressed in a Newton basis, and the associated polynomial
eigenvalue problems. Properties of the generalized ansatz spaces associated with such …