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Many state-of-the-art delineation methods rely on supervised machine learning algorithms. As a result, they require manually annotated training data, which is tedious to obtain. Furthermore, even minor classification errors may…
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…
This thesis is dedicated to developing a dilation theory for semigroups of completely positive maps. The first part treats two-parameter semigroups, and contains also contributions to dilation theory of product system representations. The…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
The lattice cell in the ${i+1}^{st}$ row and ${j+1}^{st}$ column of the positive quadrant of the plane is denoted $(i,j)$. If $\mu$ is a partition of $n+1$, we denote by $\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear…
Given a matrix $A$, a linear feasibility problem (of which linear classification is a special case) aims to find a solution to a primal problem $w: A^Tw > \textbf{0}$ or a certificate for the dual problem which is a probability distribution…
These are lectures notes on support preconditioning, originally written in 2007. The notes cover large sparse linear systems of equations, krylov subspace solvers for symmetric diagonally dominant linear systems, sparse Cholesky, support…
This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and…
It was previously known, by work of Smith-Swanson and of Sharp-Nossem, that the linear growth property of primary decompositions of Frobenius powers of ideals in rings of prime characteristic has strong connections to the localization…
The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…
We study the analytic properties of a matrix discrete system introduced in [7]. The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This…
Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…