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Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing…
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
Purpose: To evaluate an iterative learning approach for enhanced performance of Robust Artificial-neural-networks for K-space Interpolation (RAKI), when only a limited amount of training data (auto-calibration signals, ACS) are available…
Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…
Algebraic Riccati equations (AREs) have been extensively applicable in linear optimal control problems and many efficient numerical methods were developed. The most attention of numerical solutions is the (almost) stabilizing solution in…
In this work, we investigate the interval generalized Sylvester matrix equation ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$ and develop some techniques for obtaining outer estimations for the so-called united solution set of this…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
In this paper, we consider a class of nonconvex-linear minimax problems on Riemannian manifolds, which find wide applications in machine learning and signal processing. For solving this class of problems, we develop a flexible Riemannian…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
In several recent works \cite{Causley2013a}, \cite{Causley2013}, we developed a new second order, A-stable approach to wave propagation problems based on the method of lines transpose (MOL$^T$) formulation combined with alternating…
The need for large-scale electronic structure calculations arises recently in the field of material physics and efficient and accurate algebraic methods for large simultaneous linear equations become greatly important. We investigate the…
We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…
Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…
We discuss a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
This work proposes a structure-preserving model reduction method for marginally stable linear time-invariant (LTI) systems. In contrast to Lyapunov-stability-based approaches---which ensure the poles of the reduced system remain in the open…