Related papers: A simple, polynomial-time algorithm for the matrix…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
By modifying the proof of a paper by O. Bournez and M. Branicky, we establish that the Matrix Mortality Problem is decidable with any finite set of $2\times2$ matrices which has at most one invertible matrix. The same modification also…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
Consider the following Online Boolean Matrix-Vector Multiplication problem: We are given an $n\times n$ matrix $M$ and will receive $n$ column-vectors of size $n$, denoted by $v_1,\ldots,v_n$, one by one. After seeing each vector $v_i$, we…
Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of k matrices in R^{n x n} are stable. In particular, we are interested whether there exist…
A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…
We give a new procedure in Maple for finding the k-th power of a martix. The algorithm is based on the article [1].
We consider the following problem: Given a rational matrix $A \in \setQ^{m \times n}$ and a rational polyhedron $Q \subseteq\setR^{m+p}$, decide if for all vectors $b \in \setR^m$, for which there exists an integral $z \in \setZ^p$ such…
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded motion polynomials to admit factorizations into monic linear…
In this paper, we consider a problem of Lang about finiteness of torsion points on plane rational curves over $\mathbb C$, and prove some results towards a matrix analogue of this problem.
Over the last years the vertex enumeration problem of polyhedra has seen a revival in the study of metabolic networks, which increased the demand for efficient vertex enumeration algorithms for high-dimensional polyhedra given by…
A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…
In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient…
Recently, sharp matrix concentration inequalities~\cite{BBvH23,BvH24} were developed using the theory of free probability. In this work, we design polynomial time deterministic algorithms to construct outcomes that satisfy the guarantees of…
Given a multivariate real (or complex) polynomial $p$ and a domain $\cal D$, we would like to decide whether an algorithm exists to evaluate $p(x)$ accurately for all $x \in {\cal D}$ using rounded real (or complex) arithmetic. Here…
Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…
We study the problem of determining a matrix whose $k$th multiplicative compound is a prescribed matrix~$M$. The cardinality of the set of matrices whose $k$th multiplicative compound equals~$M$ is characterized in terms of $\rank(M)$. On…
This paper presents a method to analyze the powers of a given trilinear form (a special kind of algebraic constructions also called a tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication. Compared with…