Search

Your search keyword '"Gulliksson, Mårten"' showing total 49 results
Start Over Author "Gulliksson, Mårten"
49 results on '"Gulliksson, Mårten"'

2. Damped second order flow applied to image denoising

Author

Baravdish, George, Svensson, Olof, Gulliksson, Mårten, and Zhang, Ye

Subjects
Mathematics - Numerical Analysis
Abstract

In this paper, we introduce a new image denoising model: the damped flow (DF), which is a second order nonlinear evolution equation associated with a class of energy functionals of image. The existence, uniqueness and regularization property of DF are proven. For the numerical implementation, based on the St\"{o}rmer-Verlet method, a discrete damped flow, SV-DDF, is developed. The convergence of SV-DDF is studied as well. Several numerical experiments, as well as a comparison with other methods, are provided to demonstrate the feasibility and effectiveness of the SV-DDF.

Published
2018

5. Greedy Gauss-Newton algorithm for finding sparse solutions to nonlinear underdetermined systems of equations

Author

Gulliksson, Mårten and Oleynik, Anna

Subjects
Mathematics - Numerical Analysis
Abstract

We consider the problem of finding sparse solutions to a system of underdetermined nonlinear system of equations. The methods are based on a Gauss-Newton approach with line search where the search direction is found by solving a linearized problem using only a subset of the columns in the Jacobian. The choice of columns in the Jacobian is made through a greedy approach looking at either maximum descent or an approach corresponding to orthogonal matching for linear problems. The methods are shown to be convergent and efficient and outperform the $\ell_1$ approach on the test problems presented.

Published
2016

8. The Dynamical Functional Particle Method

Author

Gulliksson, Mårten, Edvardsson, Sverker, and Lind, Andreas

Subjects
Mathematics - Numerical Analysis
Abstract

We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original equations. The resulting Hamiltonian dynamical system makes it possible to apply efficient symplectic integrators. Other attractive properties of DFPM are that it has an exponential convergence rate, automatically includes a sparse formulation and in many cases can solve nonlinear problems without any special treatment. We study the convergence and convergence rate of DFPM. It is shown that for the discretized symmetric eigenvalue problems the computational complexity is given by $\mathcal{O}(N^{(d+1)/{d}})$, where \emph{d} is the dimension of the problem and \emph{N} is the vector size. An illustrative example of this is made for the 2-dimensional Schr\"odinger equation. Comparisons are made with the standard numerical libraries ARPACK and LAPACK. The conjugated gradient method and shifted power method are tested as well. It is concluded that DFPM is both versatile and efficient.

Published
2013

9. Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges.

Author

Rousse, François, Fasi, Massimiliano, Dmytryshyn, Andrii, Gulliksson, Mårten, and Ögren, Magnus

Subjects
QUANTUM theory, MATRIX decomposition, STOCHASTIC matrices, FOKKER-Planck equation, PARTICLE dynamics, PHASE space, GAUGE field theory
Abstract

The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved by benchmarking quantum dynamics of few-body systems against independent exact solutions. A diffusion gauge is implemented here as a so-called noise-matrix, which satisfies a matrix equation defined by the corresponding Fokker–Planck equation of the phase-space representation. For the physical systems with fermionic particles considered here, the numerical evaluation of the new diffusion gauges allows us to double the practical simulation time, compared with hitherto known analytic noise-matrices. This development may have far reaching consequences for future quantum dynamical simulations of many-body systems. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

12. Optimization Tools for Solving Nonlinear Ill-posed Problems

Author

Viklands, Thomas, Gulliksson, Marten, Hoffmann, K.-H., editor, Mittelmann, D., editor, Bank, R. E., editor, Kawarada, H., editor, LeVeque, R. J., editor, Verdi, C., editor, Todd, J., editor, Hoffmann, Karl-Heinz, editor, Hoppe, Ronald H. W., editor, and Schulz, Volker, editor

Published
2001
Full Text
View/download PDF

17. An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection

Author

Gulliksson, Mårten and Mazur, Stepan

Subjects
second order damped dynamical systems, singular covariance matrix, ddc:330, linear ill-posed problems, Mean-variance portfolio, C10, C44
Abstract

Covariance matrix of the asset returns plays an important role in the portfolio selection. A number of papers is focused on the case when the covariance matrix is positive definite. In this paper, we consider portfolio selection with a singular covariance matrix. We describe an iterative method based on a second order damped dynamical systems that solves the linear rank-deficient problem approximately. Since the solution is not unique, we suggest one numerical solution that can be chosen from the iterates that balances the size of portfolio and the risk. The numerical study confirms that the method has good convergence properties and gives a solution as good as or better than the constrained least norm Moore-Penrose solution. Finally, we complement our result with an empirical study where we analyze a portfolio with actual returns listed in S&P 500 index.

Published
2019

23. Finding Stationary Solutions of PDEs with Constraints using Damped Dynamical Systems

Author

Lockby, Andreas, Sandin, Patrik, Ögren, Magnus, and Gulliksson, Mårten

Subjects
Computational Mathematics, Beräkningsmatematik, PDE, constraints, dynamical system
Abstract

The dynamical functional particle method(DFPM) is a method for solving equations, e.g. PDEs, using a second order damped dynamical system. We show how the method can be extended to include constraints both explicitly as global constraints and adding the constraints as additional damped dynamical equations. These methods are implemented in Comsol and we show numerical tests for finding the stationary solution of a nonlinear heat equation with and without constraints (global and dynamical). The results show that DFPM is a very general and robust way of solving PDEs and it should be of interest to implement the approach more generally in Comsol., Metoder för att lösa ekvationer med andra ordningens dämpade dynamiska system

Published
2016

28. A modified coupled complex boundary method for an inverse chromatography problem.

Author

Xiaoliang Cheng, Guangliang Lin, Ye Zhang, Rongfang Gong, and Gulliksson, Mårten

Subjects
CHROMATOGRAPHIC analysis, INVERSE problems, ADSORPTION isotherms, BOUNDARY value problems, COMPUTATIONAL complexity, STOCHASTIC convergence
Abstract

Adsorption isotherms are the most important parameters in rigorous models of chromatographic processes. In this paper, in order to recover adsorption isotherms, we consider a coupled complex boundary method (CCBM), which was previously proposed for solving an inverse source problem [2]. With CCBM, the original boundary fitting problem is transferred to a domain fitting problem. Thus, this method has advantages regarding robustness and computation in reconstruction. In contrast to the traditional CCBM, for the sake of the reduction of computational complexity and computational cost, the recovered adsorption isotherm only corresponds to the real part of the solution of a forward complex initial boundary value problem. Furthermore, we take into account the position of the profiles and apply the momentum criterion to improve the optimization progress. Using Tikhonov regularization, the well-posedness, convergence properties and regularization parameter selection methods are studied. Based on an adjoint technique, we derive the exact Jacobian of the objective function and give an algorithm to reconstruct the adsorption isotherm. Finally, numerical simulations are given to show the feasibility and efficiency of the proposed regularization method. [ABSTRACT FROM AUTHOR]

Published
2018
Full Text
View/download PDF

30. Least Squares Approach to Inverse Problems in Musculoskeletal Biomechanics

Author

Lund Ohlsson, Marie and Gulliksson, Mårten

Subjects
Computational Mathematics, Beräkningsmatematik
Abstract

Inverse simulations of musculoskeletal models computes the internal forces such as muscle and joint reaction forces, which are hard to measure, using the more easily measured motion and external forces as input data. Because of the difficulties of measuring muscle forces and joint reactions, simulations are hard to validate. One way of reducing errors for the simulations is to ensure that the mathematical problem is well-posed. This paper presents a study of regularity aspects for an inverse simulation method, often called forward dynamics or dynamical optimization, that takes into account both measurement errors and muscle dynamics. The simulation method is explained in detail. Regularity is examined for a test problem around the optimum using the approximated quadratic problem. The results shows improved rank by including a regularization term in the objective that handles the mechanical over-determinancy. Using the 3-element Hill muscle model the chosen regularization term is the norm of the activation. To make the problem full-rank only the excitation bounds should be included in the constraints. However, this results in small negative values of the activation which indicates that muscles are pushing and not pulling. Despite this unrealistic behavior the error maybe small enough to be accepted for specific applications. These results is a starting point start for achieving better results of inverse musculoskeletal simulations from a numerical point of view.

Published
2009

35. Algorithms for overdetermined systems of equations

Author

Gulliksson, Mårten

Subjects
least squares, lp, weights, approximation, optimization, Systemvetenskap, informationssystem och informatik, Information Systems
Abstract

ix, [1] s., s. 1-7: sammanfattning, s. 8-142: 6 uppsatser digitalisering@umu

Published
1993

45. Determining the Elastic Constants of Paper with Optimization Methods.

Author

Ziqing Xie, Myung-Won, Gulliksson, Mårten, and Hägglund, Rickard

Subjects
*NEWTON-Raphson method, *CONTINUATION methods, *ISOTROPY subgroups, *FINITE element method, *MATHEMATICS
Abstract

In this article we describe a method for determining the elastic constants for paper from a measured displacement field. Our model is based on the finite element method using quadrilateral elements. A method for finding the first and second order derivatives with respect to the unknown parameters plays a crucial role in the optimization process used to solve the inverse problems in this article. To reduce the influence of the noise of the input data, an efficient continuation method is used for the regularization term in the cost function. Some numerical results for synthetic data and measurement will verify the efficiency of our approach. [ABSTRACT FROM AUTHOR]

Published
2002
Full Text
View/download PDF

46. THE USE AND PROPERTIES OF TIKHONOV FILTER MATRICES.

Author

Gulliksson, Mårten and Wedin, Per-å

Subjects
*MATRICES (Mathematics), *PERTURBATION theory, *PSEUDOINVERSES, *FILTERS (Mathematics), *APPROXIMATION theory
Abstract

We consider the concept of Tikhonov filter matrices in connection with discrete ill-posed and rank-deficient linear problems. Important properties of the Tikhonov filter matrices are given together with their filtering and regularization effects. We also present new perturbation identities for the Tikhonov regularized linear least squares problem using filter matrices generalizing well-known perturbation identities for the linear least squares problem and pseudoinverses. [ABSTRACT FROM AUTHOR]

Published
2000
Full Text
View/download PDF

47. Local results for the Gauss-Newton method on constrained rank-deficient nonlinear least squares

Author

Eriksson, Jerry and Gulliksson, Mårten E.

Abstract

A nonlinear least squares problem with nonlinear constraints may be ill posed or even rank-deficient in two ways. Considering the problem formulated as $\min_{x} 1/2| f_{2}(x) \|_{2}^{2}$ subject to the constraints $f_{1}(x) = 0$, the Jacobian $J_{1} = \partial f_{1}/ \partial x$ and/or the Jacobian $J = \partial f/ \partial x$, $f = [f_{1};f_{2}]$, may be ill conditioned at the solution. We analyze the important special case when $J_{1}$ and/or $J$ do not have full rank at the solution. In order to solve such a problem, we formulate a nonlinear least norm problem. Next we describe a truncated Gauss-Newton method. We show that the local convergence rate is determined by the maximum of three independent Rayleigh quotients related to three different spaces in $\mathbb{R}^{n}$. Another way of solving an ill-posed nonlinear least squares problem is to regularize the problem with some parameter that is reduced as the iterates converge to the minimum. Our approach is a Tikhonov based local linear regularization that converges to a minimum norm problem. This approach may be used both for almost and rank-deficient Jacobians. Finally we present computational tests on constructed problems verifying the local analysis.

Published
2004

48. Determining the Elastic Constants of Paper with Optimization Methods

Author

Xie, Ziqing, Gulliksson, MÅrten, and HAgglund, Rickard

Abstract

In this article we describe a method for determining the elastic constants for paper from a measured displacement field. Our model is based on the finite element method using quadrilateral elements. A method for finding the first and second order derivatives with respect to the unknown parameters plays a crucial role in the optimization process used to solve the inverse problems in this article. To reduce the influence of the noise of the input data, an efficient continuation method is used for the regularization term in the cost function. Some numerical results for synthetic data and measurement will verify the efficiency of our approach.

Published
2002
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results