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We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…
We propose and analyze random subspace variants of the second-order Adaptive Regularization using Cubics (ARC) algorithm. These methods iteratively restrict the search space to some random subspace of the parameters, constructing and…
The Nikiforov-Uvarov method is a simple, yet elegant and powerful method for solving second-order differential equations of generalized hypergeometric type. In the past, it has been used to solve many problems in quantum mechanics and…
Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum,…
Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their…
The adaptive cubic regularization algorithm employing the inexact gradient and Hessian is proposed on general Riemannian manifolds, together with the iteration complexity to get an approximate second-order optimality under certain…
A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free…
We analyse an algorithm of transition between Cauchy problems for second-order wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the…
One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The…
In this paper we present a tractable approach for regularizing randomly placed points, by splitting them into two subsets: the first is generated by means of the Mat\'ern hard-core point process, while the remaining points constitute the…
We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix. Iteratively, our variant only requires access to…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional…
This paper extends and analyzes the high-order kernel regularization framework of Beale & Tlupova (arXiv:2510.13639) to all four on-surface boundary integral operators of the Helmholtz Calderon calculus in three dimensions: the…
In this work, we propose a second-order accurate scheme for shallow water equations in general covariant coordinates over manifolds. In particular, the covariant parametrization in general covariant coordinates is induced by the metric…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple…
Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two…
In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…