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 …

As a crucial first step towards finding the (approximate) common roots of a (possibly
overdetermined) bivariate polynomial system of equations, the problem of determining an …

Fiedler pencils are a family of strong linearizations for polynomials expressed in the
monomial basis, that include the classical Frobenius companion pencils as special cases …

We demonstrate that the most popular variants of all common algebraic multidimensional
rootfinding algorithms are unstable by analyzing the conditioning of subproblems that are …

We perform a backward error analysis of polynomial eigenvalue problems solved via
linearization. Through the use of dual minimal bases, we unify the construction of strong …

The need to solve polynomial eigenvalue problems for matrix polynomials expressed in
nonmonomial bases has become very important. Among the most important bases in …

We consider the Keplerian distance d in the case of two elliptic orbits, ie, the distance
between one point on the first ellipse and one point on the second one, assuming they have …

We introduce and analyze numerical companion matrix methods for the reconstruction of
hypersurfaces with crossings from smooth interpolants given unordered or, without loss of …

The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense
analytical investigation and have applications in the study and simulation of the Navier …

Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or
their multivariate generalizations. We determine the dimension, degree, singular locus and …