Related papers: Efficient algorithm for the oscillatory matrix fun…
The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions $f(A)$, a question of major interest in the numerical linear algebra. To this end, we model $f(A)$ as the solution at a finite…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been developed to approximate their solutions. Although these…
We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…
We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
We develop two classes of composite moment-free numerical quadratures for computing highly oscillatory integrals having integrable singularities and stationary points. The first class of the quadrature rules has a polynomial order of…
The computation of the Mittag-Leffler (ML) function with matrix arguments, and some applications in fractional calculus, are discussed. In general the evaluation of a scalar function in matrix arguments may require the computation of…
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…
We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration…
This paper presents an efficient reversible algorithm for linear regression, both with and without ridge regression. Our reversible algorithm matches the asymptotic time and space complexity of standard irreversible algorithms for this…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…