Related papers: Hardness Results for Structured Linear Systems
This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods,…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this problem is equivalent to that of solvability of the Lie algebra…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear…
The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate…
We combine two iterative algorithms for solving large-scale systems of linear inequalities, the relaxation method of Agmon, Motzkin et al. and the randomized Kaczmarz method. In doing so, we obtain a family of algorithms that generalize and…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
The solution of large sparse linear systems is often the most time-consuming part of many science and engineering applications. Computational fluid dynamics, circuit simulation, power network analysis, and material science are just a few…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…
The solving of least square systems is a useful operation in neurocomputational modeling of learning, pattern matching, and pattern recognition. In these last two cases, the solution must be obtained on-line, thus the time required to solve…
Linear Programs (LP) are celebrated widely, particularly so in machine learning where they have allowed for effectively solving probabilistic inference tasks or imposing structure on end-to-end learning systems. Their potential might seem…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
In this paper, we present and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then present a specific version of Cramer's rule…
We consider a class of fully non-linear parabolic equations on compact Hermitian manifolds involving symmetric functions of partial Laplacians. Under fairly general assumptions, we show the long time existence and convergence of solutions.…