Convergence Properties Of Methods Research Articles

Six-Degree-of-Freedom Localization of an Untethered Magnetic Capsule Using a Single Rotating Magnetic Dipole

This paper presents a method to estimate the six-degree-of-freedom pose of a magnetic capsule, with an embedded permanent magnet and Hall-effect sensors, using a rotating dipole field. The method's convergence properties as a function of the number of distinct rotation axes of the applied field and the number of complete rotations about each axis are characterized. Across our tested workspace, the localization error was 4.9 ± 2.7 mm and 3.3 ± 1.7 degrees (mean ± standard deviation). We experimentally demonstrate this is sufficient for propulsion of a screw-type magnetic capsule through a lumen using a single dipole to both propel and localize the capsule.

Convergence of Relaxed Matrix Parallel Multisplitting Chaotic Methods forH-Matrices

Based on the methods presented by Song and Yuan (1994), we construct relaxed matrix parallel multisplitting chaotic generalized USAOR-style methods by introducing more relaxed parameters and analyze the convergence of our methods when coefficient matrices areH-matrices or irreducible diagonally dominant matrices. The parameters can be adjusted suitably so that the convergence property of methods can be substantially improved. Furthermore, we further study some applied convergence results of methods to be convenient for carrying out numerical experiments. Finally, we give some numerical examples, which show that our convergence results are applied and easily carried out.

The Weaker Convergence of Non-stationary Matrix Multisplitting Methods for Almost Linear Systems

In 1999, Arnal et al. [ Numerical linear algebra and its applications, 6(1999): 79-92] introduced the non-stationary matrix multisplitting algorithms for almost linear systems and studied the convergence of them. In this paper, we generalize Arnal’s algorithms and study the non-stationary matrix multisplitting multi-parameters methods for almost linear systems. The parameters can be adjusted suitably so that the convergence property of methods can be substantially improved. Furthermore, the convergence results of our new method in this paper are weaker than those of Arnal’s. Finally, numerical examples show that our new convergence results are better and more efficient than Arnal’s

Equilibrium in Nash differential games via Lyapunov-type iterations

This paper discusses the numerical solution of the coupled algebraic Riccati equations associated with the linear quadratic differential games. The Lyapunov iteration for solving the considered coupled equations is discussed by Li and Gajic (1994). We modify this iteration and derive the new algorithm with typically convergence properties for methods of such a type introduced in the literature. Finally, to demonstrate the efficiency of the proposed algorithms, computational examples are provided and numerical effectiveness of the considered algorithms is commented.

Plastic algorithm for adaptive vector quantisation

A plastic algorithm for building vector quantisers adaptively attains a dynamic representation of observed data; an unsupervised version of classical crossvalidation rules the algorithm's stopping condition. Combining plasticity with empirical generalisation-based control yields an adaptive methodology for VQ. The paper analyses the method's convergence properties and discusses the model's generalisation performance. Experimental results on synthetic and real, complex testbeds support the model's validity.

An efficient solution of weak-collision master equations in thermal unimolecular reaction rate theory

A new finite-basis-set method of solving the weak-collision master equation of thermal unimolecular reactions in the general pressure regime is presented. Consecutive sections of the equilibrium probability density are used as basis functions. Significant advantages in terms of efficiency and applicability are obtained. Representative calculations are performed to illustrate the method's convergence properties and storage requirements. Calculations of collisional efficiency factors in the low-pressure limit β 0 and weak-collision broadening factors F W C (ω) are performed to offer a simple concise representation of weak-collision effects. It is noted that weak-collision effects can be incorporated into fall-off curves with an accuracy of within an order of magnitude by simple scaling of the strong-collision fall-off curves. However, for accurate representation of weak-collision effects the weak-collision broadening must be taken into account.