In this paper, the nonlinear U model with time-varying coefficients is investigated and transformation of accomplished by Newton iterative algorithm. Based on non...

Based on the algebraic transformation of a randomly switched linear measurement equation to a nonlinear, yet deterministic equation, an asymptotic observer is constructed for a class of systems encountered in manufacturing, telecommunications, and embedded control applications. The observer is shown to be locally exponentially stable for any arbitrary switching sequence, and combines the algebr...

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton’s gravitational field equations. It is shown, in particular, that the maximal symmetry group of the sta...

A particle system with a (2+1)D exotic Newton-Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic oscillators) are separated by the critical phase (one-mode oscillator), and are related by a duality ...

The finite element setting for nonlinear elliptic PDEs directly leads to the minimization of convex functionals. Uniform ellipticity of the underlying PDE shows up as strict convexity of the arising nonlinear functional. The paper analyzes computational variants of Newton’s method for convex optimization in an affine conjugate setting, which reflects the appropriate affine transformation behavi...

The Helmert transformation is used in geodesy. It transforms a set of points into another by rotation, scaling and translation. When both sets of points are given, then least squares can be used to solve the inverse problem of determining the parameters. In particular, the parameters of the so-called 7 parameter transformation can be obtained by standard methods. In this note, it is shown how a...

This paper presents explicit formulae for multivariate Maclaurin-Lagrange M : Kn1×n2×...×nd → Kn1×n2×...×nd and Maclaurin-Newton P : Kn1×n2×...×nd → Kn1×n2×...×nd transformations with respect to points whose coordinates form geometric sequences. Moreover, efficient algorithms for these transformations are given. Both of them perform computations with a running time of O (∏d j=1 nj · log ∏d j=1 ...

A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type methods can be applied. The method is genera...

Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton’s method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov decision processes (MDPs). We first ana...