Numerical Improvements to Closed-Loop Ascent Guidance

2011 ◽  
Vol 383-390 ◽  
pp. 5076-5081
Author(s):  
Bin Feng Pan ◽  
Shuo Tang
Keyword(s):  
Shooting Method ◽  
Closed Loop ◽  
Gaussian Elimination ◽  
Multiple Shooting ◽  
3 Dimensional ◽  
Root Finding ◽  
Marquardt Method ◽  
Multiple Shooting Method ◽  
Root Finding Method ◽  
Finding Method

This paper presents numerical enhancements for optimal closed-loop ascent guidance through atmospheric. For 3-dimensional ascent formulation, optimal endo-atmospheric ascent trajectory is numerically obtained by the relaxation approach, and the exo-atmospheric ascent trajectory is generated by an analytical multiple-shooting method. A new root-finding method based on double dogleg method and More’s Levenberg-Marquardt method with Gaussian elimination is presented. The simulation results indicate that our new algorithm has remarkable computation and convergence performances.

scholarly journals Multiple shooting method in stability analysis of non-prismatic multi-segment columns

2013 ◽  
Vol 12 (4) ◽  
pp. 225-232
Author(s):  
Ryszard Hołubowski ◽  
Andrzej Merena
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Shooting Method ◽  
High Efficiency ◽  
Variable Coefficients ◽  
Multiple Shooting ◽  
System Of Differential Equations ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Multiple Shooting Method

The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.

Parallel Root-Finding Method for LPC Analysis of Speech

2004 ◽  
pp. 529-536
Author(s):  
Juan-Luis García Zapata ◽  
Juan Carlos Díaz Martín ◽  
Pedro Gómez Vilda
Keyword(s):  
Root Finding ◽  
Root Finding Method ◽  
Finding Method

Evaluation of an S-system root-finding method for estimating parameters in a metabolic reaction model

2018 ◽  
Vol 301 ◽  
pp. 21-31 ◽  
Author(s):  
Michio Iwata ◽  
Atsuko Miyawaki-Kuwakado ◽  
Erika Yoshida ◽  
Soichiro Komori ◽  
Fumihide Shiraishi
Keyword(s):  
Reaction Model ◽  
Metabolic Reaction ◽  
Root Finding ◽  
Root Finding Method ◽  
Finding Method

scholarly journals Visual Analysis of the Newton’s Method with Fractional Order Derivatives

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1143 ◽  
Author(s):  
Krzysztof Gdawiec ◽  
Wiesław Kotarski ◽  
Agnieszka Lisowska
Keyword(s):  
Visual Analysis ◽  
Dynamic Properties ◽  
Speed Of Convergence ◽  
Polynomial Zeros ◽  
Polynomial Roots ◽  
Root Finding ◽  
Root Finding Method ◽  
Finding Method ◽  
Number Of Iterations ◽  
Basins Of Attractions

The aim of this paper is to investigate experimentally and to present visually the dynamics of the processes in which in the standard Newton’s root-finding method the classic derivative is replaced by the fractional Riemann–Liouville or Caputo derivatives. These processes applied to polynomials on the complex plane produce images showing basins of attractions for polynomial zeros or images representing the number of iterations required to obtain polynomial roots. These latter images were called by Kalantari as polynomiographs. We use both: the colouring by roots to present basins of attractions, and the colouring by iterations that reveal the speed of convergence and dynamic properties of processes visualised by polynomiographs.

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