Related papers: Lanczos-like algorithm for the time-ordered expone…

We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…

The backward problem for subdiffusion equation with the fractional Riemann-Liouville time-derivative of order ? 2 (0; 1) and an arbitrary positive self-adjoint operator A is considered. This problem is ill-posed in the sense of Hadamard due…

We develop a weakest-precondition-style calculus \`a la Dijkstra for reasoning about amortized expected runtimes of randomized algorithms with access to dynamic memory - the $\textsf{aert}$ calculus. Our calculus is truly quantitative, i.e.…

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…

For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi >0$. For Markov processes we give additional conditions under which the…

We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a…

The main goal of this paper is to achieve a simultaneous treatment of the even and odd truncated matricial Stieltjes moment problems in the most general case. These results are generalizations of results of Chen and Hu [5,17] which…

Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulting many innovative and important advancements which would…

We propose potential-based analyses for first-order algorithms applied to constrained and composite minimization problems. We first propose ``idealized'' frameworks for algorithms in the strongly and non-strongly convex cases and argue…

It is known that Green's functions can be expressed as continued fractions; the content at the $n$-th level of the fraction is encoded in a coefficient $b_n$, which can be recursively obtained using the Lanczos algorithm. We present a…

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…

In this work, forward and inverse problems for a time-fractional pseudo-parabolic equation $D_t^{\rho} [u(t) + \mu Au(t)] + \sigma(t) Au(t) = r(t)g$ are investigated in a Hilbert space, where $A$ is an unbounded, positive, self-adjoint…

We propose a new concept of a relatively inexact stochastic subgradient and present novel first-order methods that can use such objects to approximately solve convex optimization problems in relative scale. An important example where…

In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed…

We present a derivation of the Landau-Zener solution through the explicit evaluation of the time ordered propagator. The result is exact and does not involve the solution of the differential equation for the spin amplitudes.

In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…

This paper adapts look-ahead and backward finite difference formulas to compute future eigenvectors and eigenvalues of piecewise smooth time-varying symmetric matrix flows $A(t)$. It is based on the Zhang Neural Network (ZNN) model for…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…

A new procedure is constructed by means of APS in APLAN language. The procedure solves the initial-value problem for linear differential equations of order $k$ with polynomial coefficients and regular singularity in the initialization point…