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Related papers: A Gauss Elimination Method for Resonances

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Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.

Optimization and Control · Mathematics 2011-12-06 Sébastien Marinesque

High intensity focused ultrasound is a non-invasive method for treatment of diseased tissue that uses a beam of ultrasound to generate heat within a small volume. A common challenge in application of this technique is that heterogeneity of…

Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using…

Numerical Analysis · Mathematics 2023-02-27 Nam Van Tran , Imme van den Berg

This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [Mol. Phys., 111 2086 (2013)] when the Schr\"odinger equation is solved variationally with explicitly correlated Gaussian…

Computational Physics · Physics 2018-04-25 Andrea Muolo , Edit Mátyus , Markus Reiher

Gaussian elimination (GE) is the archetypal direct algorithm for solving linear systems of equations and this has been its primary application for thousands of years. In the last decade, GE has found another major use as an iterative…

Numerical Analysis · Mathematics 2016-02-23 Alex Townsend

The numerical extraction of resonant states of open quantum systems is usually a difficult problem. Regularization techniques, such as the mapping to complex coordinates or the addition of Complex Absorbing Potentials are typically…

Materials Science · Physics 2015-04-03 Luigi Genovese , Alessandro Cerioni , Maxime Morinière , Thierry Deutsch

The calculation of minimum energy paths for transitions such as atomic and/or spin re-arrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to…

Chemical Physics · Physics 2017-03-31 Olli-Pekka Koistinen , Emile Maras , Aki Vehtari , Hannes Jónsson

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time's spending. Further, both of…

Mathematical Software · Computer Science 2015-04-28 Anton Kochnev , Nicolai Savelov

The explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure for the solution of systems of linear equations is applied to error analysis. Stability conditions in terms of relative…

Combinatorics · Mathematics 2020-10-30 Nam Van Tran , Júlia Justino , Imme van den Berg

We propose a simple and straightforward method based on Wronskians for the calculation of bound--state energies and wavefunctions of one--dimensional quantum--mechanical problems. We explicitly discuss the asymptotic behavior of the…

Quantum Physics · Physics 2015-05-27 Francisco M. Fernández

A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…

Analysis of PDEs · Mathematics 2011-02-15 Jean-Luc Akian , Radjesvarane Alexandre , Salma Bougacha

A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…

Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…

Applications · Statistics 2023-04-10 Agnimitra Dasgupta , Carlo Graziani , Zichao Wendy Di

Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…

Quantum Physics · Physics 2021-07-09 Robbie Thomson Ireland

A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.

High Energy Physics - Theory · Physics 2007-05-23 R. Banerjee

In this paper we studied approximate solutions of the radial Schr\"odinger equation with the attractive Gaussian potential. We used asymptotic iteration method and variational method in order to obtain energy eigenvalues for any $n$ and $l$…

Quantum Physics · Physics 2019-03-12 Halil Mutuk

A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the…

High Energy Physics - Phenomenology · Physics 2009-01-07 Luca Marotta , Fabio Siringo

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…

Machine Learning · Statistics 2023-07-03 Adrian G. Wills , Johannes Hendriks , Christopher Renton , Brett Ninness

A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…

General Relativity and Quantum Cosmology · Physics 2017-02-08 Nigel T. Bishop , Luciano Rezzolla

Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…

Information Theory · Computer Science 2010-11-04 Mr. Chong Han , Dr. Ido Nevat , Dr. Gareth Peters , Prof. Jinhong Yuan
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