相关论文: Solution of Matrix Dyson Equation for Random Matri…

In this article we prove the global existence of weak solutions to an initial boundary value problem with an exponential and p-Laplacian nonlinearity. The equation is a continuum limit of a family of kinetic Monte Carlo models of crystal…

When solving partial differential equations (PDEs) using finite difference or finite element methods, efficient solvers are required for handling large sparse linear systems. In this paper, a recursive sparse LU decomposition for matrices…

We derive the divergence-kernel formula for the linear response of random dynamical systems. Specifically, the pathwise expression is for the parameter-derivative of the marginal or stationary density, not an averaged observable. Our…

In this paper, we are concerned with the asymptotic behavior of solutions of M1 model on quadrant. From this model, combined with damped compressible Euler equations, a more general system is introduced. We show that the solutions to the…

This paper is concerned with the multi-dimensional compressible Euler equations with time-dependent damping of the form $-\frac{\mu}{(1+t)^\lambda}\rho\boldsymbol u$ in $\mathbb R^n$, where $n\ge2$, $\mu>0$, and $\lambda\in[0,1)$. When…

Let $(M, \omega)$ be a compact connected K\"ahler manifold of complex dimension four and let $[\chi] \in H^{1,1}(M; \mathbb{R})$. We confirmed the conjecture by Collins--Jacob--Yau [arXiv:1508.01934] of the solvability of the deformed…

In a Hilbert setting, we introduce a new dynamical system and associated algorithms for solving monotone inclusions by rapid methods. Given a maximal monotone operator $A$, the evolution is governed by the time dependent operator $I -(I +…

We introduce a (variation of quadrics) ansatz for constructing explicit, real-valued solutions to broad classes of complex Hessian equations on domains in $\mathbb{C}^{n+1}$ and real Hessian equations on domains in $\mathbb{R}^{n+1}$. In…

Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…

We consider a problem of linear model selection in the presence of both continuous and categorical predictors. Feasible models consist of subsets of numerical variables and partitions of levels of factors. A new algorithm called delete or…

We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In…

A modification of Newton's method for solving systems of $n$ nonlinear equations is presented. The new matrix-free method relies on a given decomposition of the invertible Jacobian of the residual into invertible sparse local Jacobians…

The Dyson Brownian Motion (DBM) describes the stochastic evolution of $N$ points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler…

On the basis of pure gauge sector of Blaizot-Iancu equation, we derive kinetic equation of Boltzmann type, taking into account 2n+2-colorless plasmon decay processes, n=1,2,.... Using so-called Tsytovich correspondence principle, a direct…

This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator…

We present a sparse Gauss-Newton solver for accelerated sensitivity analysis with applications to a wide range of equilibrium-constrained optimization problems. Dense Gauss-Newton solvers have shown promising convergence rates for inverse…

We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…

A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…

We consider the decision problem for quantifier-free formulas whose atoms are linear inequalities interpreted over the reals or rationals. This problem may be decided using satisfiability modulo theory (SMT), using a mixture of a SAT solver…

We present a new, practical algorithm for computing the determinant of a non-singular dense, uniform matrix over Z; the aim is to achieve better practical efficiency, which is always at least as good as currently known methods. The…