Related papers: A Systematic Framework for Stable and Cost-Efficie…
We consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimates by equilibrated fluxes, i.e., vector-valued mapped…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials…
Single-input eigenvalue assignment problem (SEVAS) for dense (non-sparse) weakly controllable pairs A,B using Ackermann's formula is revisited. Factorizations are presented that are interpreted using quotient (factor) vector spaces.…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
Orthogonal polynomials of several variables have a vector-valued three-term recurrence relation, much like the corresponding one-dimensional relation. This relation requires only knowledge of certain recurrence matrices, and allows simple…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
We present a novel classical algorithm designed to learn the stabilizer group -- namely the group of Pauli strings for which a state is a $\pm 1$ eigenvector -- of a given Matrix Product State (MPS). The algorithm is based on a clever and…
We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…
The dominant cost in solving least-square problems using Newton's method is often that of factorizing the Hessian matrix over multiple values of the regularization parameter ($\lambda$). We propose an efficient way to interpolate the…
The aim of this paper is to present a symbolic computational algorithm that will allow us to deal with the feedback stabilization problem for continuous nonlinear polynomial systems. The overall approach is based on a methodology that…
For piecewise-linear maps the stable and unstable manifolds of hyperbolic periodic solutions are themselves piecewise-linear. Hence compact subsets of these manifolds can be represented using polytopes (i.e. polygons, in the case of…
The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the…
Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…
A standard approach to compute the roots of a univariate polynomial is to compute the eigenvalues of an associated \emph{confederate} matrix instead, such as, for instance the companion or comrade matrix. The eigenvalues of the confederate…
We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy based solvers in terms of decorated graphs. Under the…
We provide a computer-assisted approach to ensure that a given continuous or discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov…