Search results for "iterative method"
showing 10 items of 135 documents
Recurrence relations for rational cubic methods I: The Halley method
1990
In this paper we present a system of a priori error bounds for the Halley method in Banach spaces. Our theorem supplies sufficient conditions on the initial point to ensure the convergence of Halley iterates, by means of a system of “recurrence relations”, analogous to those given for the Newton method by Kantorovich, improving previous results by Doring [4]. The error bounds presented are optimal for second degree polynomials. Other rational cubic methods, as the Chebyshev method, will be treated in a subsequent paper.
Optimal Design of Trusses According to a Plastic Shakedown Criterion
2004
The optimal design of elastic-perfectly plastic truss structures subjected to quasi-statically loads variable within a given load domain is studied. The actions are given as the combination of fixed load and perfect cyclic load. Suitably chosen load multipliers are given. A minimum volume formulation of the design problem with assigned limit load multiplier is developed and it is provided on the grounds of a statical approach as well as of a kinematical approach. The incremental collapse (ratchetting) of the optimal structure is prevented, as long as the loads are not greater than some prescribed values, by special constraints suitably introduced in the search problem. The Kuhn-Tucker equat…
Evaluating a hierarchical approach to landscape level harvest scheduling
2018
Forest planning at the landscape level has the potential to become a large intractable problem. In Finland, Metsähallitus (the state enterprise that manages federally owned land) creates strategic plans to determine the appropriate harvest level. While these plans are feasible, they are not implementable in practice as the harvests are scattered temporally and spatially. Requiring that harvests be organized both temporally and spatially for practical implementation can result in an intractable problem. Through a hierarchical approach, the problem can be organized into steps in which the intractable problem is broken down into smaller easily solvable parts. As an approximation technique, the…
Uncertainty management in the measurements for the electric power quality analysis
2014
The paper deals with the uncertainty estimation in the measurements performed to assess the electric power quality. In a first steps, all the error sources, which give a significant contribution to the combined uncertainty associated to the measurement results, are identified. Successively, in order to analyze how the errors combine and propagate through the measurement chain, four approaches are proposed and validated. These approaches entail a greater and greater uncertainty overestimation, but, at the same time, require less and less time and resources. Therefore, the four methodologies are perfectly adequate for the implementation of the PUMA (Procedure for Uncertainty Management) metho…
Integrating risk management tools for regional forest planning : an interactive multiobjective value at risk approach
2018
In this paper, we present an approach employing multiobjective optimization to support decision making in forest management planning under risk. The primary objectives are biodiversity and timber cash flow, evaluated from two perspectives: the expected value and the value-at-risk (VaR). In addition, the risk level for both the timber cash flow and biodiversity values are included as objectives. With our approach, we highlight the trade-off between the expected value and the VaR, as well as between the VaRs of the two objectives of interest. We employ an interactive method in which a decision maker iteratively provides preference information to find the most preferred management plan and lea…
On the local and semilocal convergence of a parameterized multi-step Newton method
2020
Abstract This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including the discretization of ordinary differential equations, integral equations, integro-differential equations or partial differential equations. Moreover, multi-step iterative methods are computationally attractive.
Scheduled Relaxation Jacobi method: improvements and applications
2016
Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficien…
An iterative method in a probabilistic approach to the spectral inverse problem - Differential emission measure from line spectra and broadband data
2010
Inverse problems are of great importance in astrophysics for deriving information about the physical characteristics of hot optically thin plasma sources from their EUV and X-ray spectra. We describe and test an iterative method developed within the framework of a probabilistic approach to the spectral inverse problem for determining the thermal structures of the emitting plasma. We also demonstrate applications of this method to both high resolution line spectra and broadband imaging data. Our so-called Bayesian iterative method (BIM) is an iterative procedure based on Bayes' theorem and is used to reconstruct differential emission measure (DEM) distributions. To demonstrate the abilities …
Harmonic solution of semiconductor transport equations for microwave and millimetre-wave device modelling
2004
The transport equations for charges in a semiconductor have been solved for a periodic voltage excitation by means of a harmonic approach, for modelling of microwave and millimetre-wave active devices. The solution is based on the expansion of the unknown physical quantities in Fourier series in the time domain, and on the discretisation in the space domain. A Waveform-Balance technique in the time domain is used to solve the resulting non-linear equations system. In this way the time step is determined only by Nyquist's sampling requirements at the operating frequency, irrespective of the relaxation times of the semiconductor. This approach allows for a longer time step, and therefore a sh…
The CC3 model : An iterative coupled cluster approach including connected triples
1997
An alternative derivation of many-body perturbation theory (MBPT) has been given, where a coupled cluster parametrization is used for the wave function and the method of undetermined Lagrange multipliers is applied to set up a variational coupled cluster energy expression. In this variational formulation, the nth-order amplitudes determine the energy to order 2n+1 and the nth-order multipliers determine the energy to order 2n+2. We have developed an iterative approximate coupled cluster singles, doubles, and triples model CC3, where the triples amplitudes are correct through second order and the singles amplitudes are treated without approximations due to the unique role of singles as appro…