Numerical Analysis
For any matrix A in R^(m x n) of rank \rho, we present a probability distribution over the entries of A (the element-wise leverage scores of equation (2)) that reveals the most influential entries in the matrix. From a theoretical…
This paper presents a comparison of the quality of randomness of D sequences based on diehard tests. Since D sequences can model any random sequence, this comparison is of value beyond this specific class.
A parallelization of a sweeping preconditioner for 3D Helmholtz equations without large cavities is introduced and benchmarked for several challenging velocity models. The setup and application costs of the sequential preconditioner are…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work. The heart of our algorithm is a construction of a…
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…
Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing.…
In this paper, we consider the problem of recovering an unknown sparse matrix X from the matrix sketch Y = AX B^T. The dimension of Y is less than that of X, and A and B are known matrices. This problem can be solved using standard…
In the context of unconstraint numerical optimization, this paper investigates the global linear convergence of a simple probabilistic derivative-free optimization algorithm (DFO). The algorithm samples a candidate solution from a standard…
This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods (Sandu and Guenther, 2013). Multirate schemes use different step sizes for different components and for…
This work generalizes the additively partitioned Runge-Kutta methods by allowing for different stage values as arguments of different components of the right hand side. An order conditions theory is developed for the new family of…
Large molecular dynamics simulations (millions of atoms, tens of microseconds, thousands of processors) hit the strong scalability wall: simulation on twice as many processors does not take half the time. Inspired by large N-body space…
The eigenvalue problem of the Laplace-Beltrami operators on curved surfaces plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve this…
This report proposes a novel framework for a rigorous robustness analysis of stochastic biochemical systems. The technique is based on probabilistic model checking. We adapt the general definition of robustness introduced by Kitano to the…
Standard explicit schemes for parabolic equations are not very convenient for computing practice due to the fact that they have strong restrictions on a time step. More promising explicit schemes are associated with explicit-implicit…
In this study, we present a method to measure changes over time of fractal dimension. We confirmed that our method can calculate the fractal dimension with the same precision as conventional methods, and tracking performance of our method…
Sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it…
We propose in this paper a novel inverse tangent transverse shear deformation formulation for functionally graded material (FGM) plates. The isogeometric finite element analysis (IGA) of static, free vibration and buckling problems of FGM…