Related papers: An improved Talbot method for numerical Laplace tr…
The Laplace approximation (LA) to posteriors is a ubiquitous tool to simplify Bayesian computation, particularly in the high-dimensional settings arising in Bayesian inverse problems. Precisely quantifying the LA accuracy is a challenging…
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…
In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible…
We calculate the solution of the Bagley-Torvik equation for arbitrary initial conditions and arbitrary external force as the sum of two terms. The first one is a linear combination of exponentials with error functions, and the second one is…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral…
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
New numerical algorithms based on rational functions are introduced that can solve certain Laplace and Helmholtz problems on two-dimensional domains with corners faster and more accurately than the standard methods of finite elements and…
In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…
The montecarlo method, which is quite commonly used to solve maximum entropy problems in statistical physics, can actually be used to solve inverse problems in a much wider context. The probability distribution which maximizes entropy can…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.
Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Among the numerical inverse Laplace transformation (NILT) methods, those that belong to the Abate-Whitt framework (AWF) are considered to be the most efficient ones currently. It is a characteristic feature of the AWF NILT procedures that…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
Unoriented surface reconstructions based on the Gauss formula have attracted much attention due to their elegant mathematical formulation and excellent performance. However, the isotropic characteristics of the formulation limit their…