On the stability of a class of convergence acceleration methods for power series

1984 ◽  
Vol 24 (4) ◽  
pp. 510-519 ◽  
Author(s):  
Sven-Åke Gustafson
Keyword(s):  
Power Series ◽  
Convergence Acceleration ◽  
Acceleration Methods ◽  
The Stability

Attitude reconstruction from strap-down rate gyros using power series

2021 ◽  
pp. 1-19
Author(s):  
Habib Ghanbarpourasl
Keyword(s):  
Power Series ◽  
Taylor Series ◽  
Direction Cosine ◽  
Analytical Description ◽  
Double Precision ◽  
Angular Velocity Vector ◽  
Higher Order Terms ◽  
Direction Cosine Matrix ◽  
The Stability ◽  
Better Than

Abstract This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

Dipole Admittances Obtained via Convergence Acceleration Methods: Fast and Accurate Computations

2020 ◽  
Vol 62 (3) ◽  
pp. 30-38
Author(s):  
Achilleas Marinakis ◽  
Panagiotis J. Papakanellos ◽  
George Fikioris
Keyword(s):  
Convergence Acceleration ◽  
Acceleration Methods ◽  
Accurate Computations

On the Torus Flow Y′ = A + B cos Y + C cos X and its Relation to the Quasiperiodic Mathieu Equation

1999 ◽  
Author(s):  
Stephanie Mason ◽  
Richard Rand
Keyword(s):  
Power Series ◽  
Numerical Integration ◽  
Mathieu Equation ◽  
Series Solutions ◽  
Power Series Solutions ◽  
The Stability

Abstract We obtain power series solutions to the “abc equation” dydx=a+bcosy+ccosx, valid for small c, and for small b. This equation is shown to determine the stability of the quasiperiodic Mathieu equation, z¨+(δ+ϵA1cost+ϵA2cosωt)z=0, in the small ϵ limit. Perturbation results of the abc equation are shown to compare favorably to numerical integration of the quasiperiodic Mathieu equation.

scholarly journals Milestones in the Development of Iterative Solution Methods

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
Owe Axelsson
Keyword(s):  
Degrees Of Freedom ◽  
Iterative Solution ◽  
Convergence Acceleration ◽  
Optimal Order ◽  
Defect Correction ◽  
Acceleration Methods ◽  
Solution Methods ◽  
Iteration Methods ◽  
Iterative Solution Methods ◽  
Linear Systems Of Equations

Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defect-correction type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR) method. Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iteration methods and preconditioning methods of various forms. A major strive has been to find methods with a total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some of them are presented in greater detail.

scholarly journals Solvating power series of electrolyte solvents for lithium batteries

2019 ◽  
Vol 12 (4) ◽  
pp. 1249-1254 ◽  
Author(s):  
Chi-Cheung Su ◽  
Meinan He ◽  
Rachid Amine ◽  
Tomas Rojas ◽  
Lei Cheng ◽  
...  
Keyword(s):  
Power Series ◽  
Redox Potential ◽  
Solid Electrolyte ◽  
Lithium Batteries ◽  
Critical Role ◽  
The Stability

From dictating the redox potential of electrolyte solvents to shaping the stability of solid-electrolyte interfaces, solvation plays a critical role in the electrochemistry of electrolytes.

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