Higher order method for non linear equations resolution: application to mobile robot control

2007 ◽  
Author(s):  
Aldo Balestrino ◽  
Lucia Pallottino
Keyword(s):  
Mobile Robot ◽  
Robot Control ◽  
Linear Equations ◽  
Higher Order ◽  
Order Method ◽  
Non Linear ◽  
Higher Order Method ◽  
Mobile Robot Control ◽  
Non Linear Equations

scholarly journals Basic Steffensen's Method of Higher-Order Convergence

2021 ◽  
Vol 8 (4) ◽  
pp. 184-191
Author(s):  
Ola A. Ashour
Keyword(s):  
Fourth Order ◽  
Linear Equations ◽  
Higher Order ◽  
Order Convergence ◽  
Steffensen’S Method ◽  
Non Linear ◽  
Higher Order Convergence ◽  
Non Linear Equations

In this paper, we introduce a new analog of a variant of Steffensen's method of fourth-order convergence for solving non-linear equations based on the q-deference operator.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

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