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The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
Both unitary evolution and the effects of dissipation and decoherence for a general three-level system are of widespread interest in quantum optics, molecular physics, and elsewhere. A previous paper presented a technique for solving the…
The randomized Kaczmarz algorithm has received considerable attention recently because of its simplicity, speed, and the ability to approximately solve large-scale linear systems of equations. In this paper we propose randomized double and…
We present a Lanczos tau method for the approximation and optimization of the $H^2$-norm of time-delay systems described by semi-explicit delay differential algebraic equations. The soundness of this approach is proven under the assumption…
In this manuscript, we deal with some particular type of homogeneous first order linear systems with variable coefficients, in which we provide qualitative properties of the solution. When the coefficients of the indeterminate functions are…
This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually…
We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good…
We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and…
The systematization of the purely Lagrangean approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
Based on the work of Chen and Its [{\em J. Approx. Theory} {\bf 162} ({2010}) {270--297}], we further study orthogonal polynomials with respect to the singularly perturbed Laguerre weight $w(x;t,\alpha) = {x^\alpha}{\mathrm e^{-…
In this paper, we study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). The coupling considered here is time-varying in both the network structure and…
We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast…
In this paper, we first prove that when the associated graph of a polynomial set is chordal, a particular triangular set computed by a general algorithm in top-down style for computing the triangular decomposition of this polynomial set has…
Lagrangian coherent structures (LCSs) are material surfaces that shape finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from…
We reformulate the Lanczos tau method for the discretization of time-delay systems in terms of a pencil of operators, allowing for new insights into this approach. As a first main result, we show that, for the choice of a shifted Legendre…
A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel…