Related papers: A note on algebraic Riccati equations associated w…
We revisit a formula that connects the minimal ranks of triangular parts of a matrix and its inverse and relate the result to structured rank matrices. We also address the generic minimal rank problem.
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…
The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…
In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied…
We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this…
This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…
We show how to reduce the nonlinear Wei-Norman equations, expressing the solution of a linear system of non-autonomous equations on a Lie algebra, to a hierarchy of matrix Riccati equations using the cominuscule induction. The construction…
We are interested in finding a solution to the tensor complementarity problem with a strong M-tensor, which we call the M-tensor complementarity problem. We propose a lower dimensional linear equation approach to solve that problem. At each…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…
In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012--4024, with respect to the convergence of the accelerated Riccati iteration method for solving the…
We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum of T: all countable models of T are recursively presentable; none of…
In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and $q$-regular sequences (in the sense of Allouche and Shallit) via their linear representations. In particular, we…
Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches to solve these in case of small-scale dense coefficients,…
In this paper we discuss the notion of reducibility for matrix weights and introduce a real vector space $\mathcal C_\mathbb{R}$ which encodes all information about the reducibility of $W$. In particular a weight $W$ reduces if and only if…
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
Using the relationship between totally nonnegative matrices and directed acyclic weighted planar networks, we show that $2\times 2$ minors of minor matrices of totally nonnegative matrices are also nonnegative. We give a combinatorial…
This paper investigates minimax quadratic programming problems with coupled inequality constraints. By leveraging a duality theorem, we develop a dual algorithm that extends the dual active set method to the minimax setting, transforming…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…