Related papers: Resilient asynchronous primal Schur method
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
We consider the uniqueness of solution (i.e., nonsingularity) of systems of $r$ generalized Sylvester and $\star$-Sylvester equations with $n\times n$ coefficients. After several reductions, we show that it is sufficient to analyze periodic…
We consider the solution of the Sylvester equation $AX+XB=C$ in mixed precision. We derive a new iterative refinement scheme to solve perturbed quasi-triangular Sylvester equations; our rounding error analysis provides sufficient conditions…
In this work, we introduce a quadratically convergent and dynamically consistent integrator specifically designed for the replicator dynamics. The proposed scheme combines a two-stage rational approximation with a normalization step to…
The primal-dual distributed optimization methods have broad large-scale machine learning applications. Previous primal-dual distributed methods are not applicable when the dual formulation is not available, e.g. the sum-of-non-convex…
A preconditioning theory is presented which establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational…
Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton's method, they have experienced a rise in popularity recently in the context of problems for which Newton's method…
In this paper, we introduce a novel numerical approach for approximating the SIR model in epidemiology. Our method enhances the existing linearization procedure by incorporating a suitable relaxation term to tackle the transcendental…
This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…
We construct discrete time Markov chains that preserve the class of Schur processes on partitions and signatures. One application is a simple exact sampling algorithm for q^{volume}-distributed skew plane partitions with an arbitrary back…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…
We show how a scalable preconditioner for the primal discontinuous Petrov-Galerkin (DPG) method can be developed using existing algebraic multigrid (AMG) preconditioning techniques. The stability of the DPG method gives a norm equivalence…
In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partially. At the same time, non-computed entries are set to…
The Global-Local non-invasive coupling is an improvement of the submodeling technique, which permits to locally enhance structure computations by introducing patches with refined models and to take into accounts all the interactions. In…
A pseudo-spectral method with an absorbing outer boundary is used to solve a set of the time-dependent force-free equations. In the method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH)…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations,…