On the Convergence of Inexact Newton Methods

Idema, Reijer; Lahaye, Domenico; Vuik, C.

doi:10.1007/978-3-319-10705-9_35

Cited by 6 publications

(5 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We note that the choices for ¹Á k º in Theorem 5 extend the ones in [8,[15][16][17][18]20], in particular, for the case of Q-linear convergence theory.…”

Section: Remarkmentioning

confidence: 90%

“…We start by giving our feasible projected Newton–Krylov method as follows. We remark that the forcing term { η k } in our feasible projected Newton–Krylov method can be chosen according to the strategy for inexact Newton method without projection in , because the nonexpansiveness of the projection operator does not affect the local convergence of the projected Newton method. Thus, inequality (5) is always satisfied as iterative point x k is close enough to the solution of F ( x ) on Ω, see Theorem stated in the succeeding text.…”

Section: Feasible Projected Newton–krylov Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Globalization technique for projected Newton–Krylov methods

Chen

Vuik

2016

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYLarge-scale systems of nonlinear equations appear in many applications. In various applications, the solution of the nonlinear equations should also be in a certain interval. A typical application is a discretized system of reaction diffusion equations. It is well known that chemical species should be positive otherwise the solution is not physical and in general blow up occurs. Recently, a projected Newton method has been developed, which can be used to solve this type of problems. A drawback is that the projected Newton method is not globally convergent. This motivates us to develop a new feasible projected Newton-Krylov algorithm for solving a constrained system of nonlinear equations. Combined with a projected gradient direction, our feasible projected Newton-Krylov algorithm circumvents the non-descent drawback of search directions which appear in the classical projected Newton methods. Global and local superlinear convergence of our approach is established under some standard assumptions. Numerical experiments are used to illustrate that the new projected Newton method is globally convergent and is a significate complementarity for Newton-Krylov algorithms known in the literature.

show abstract

“…We note that the choices for ¹Á k º in Theorem 5 extend the ones in [8,[15][16][17][18]20], in particular, for the case of Q-linear convergence theory.…”

Section: Remarkmentioning

confidence: 90%

Section: Feasible Projected Newton–krylov Methodsmentioning

confidence: 99%

Globalization technique for projected Newton–Krylov methods

Chen

Vuik

2016

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…The presence of the first and second derivatives shows that this method is more suitable for continuous signals. A detailed discussion of the method, together with many applications, can be found in [20][21].…”

Section: Fault Tolerant Control Structurementioning

confidence: 99%

Fault Tolerant Control of PMSM Drive Using Luenberger and Adaptive Back-EMF Observers

Medjmadj¹

2019

EJEE

View full text Add to dashboard Cite

In this paper, we propose to design a sensorless controller that can cope both with performance and robustness by the hybridization of two controllers. The strategy introduced in this paper includes the sensorless active fault tolerant controller of the PMSM drive at high speed. It is built with the combination of a vector controller, two virtual sensors: Luenberger and adaptive back-EMF observers, and a voting algorithm using Newton-Raphson method. Simulation results are provided to verify effectiveness of the proposed strategy of a 1kW PMSM motor driven by fault tolerant control in case of position sensor outage.

show abstract

“…In the proposed algorithm for estimation of the unknown parameters of the processed power signal, an iterative scheme is not applied on the Newton-Raphson method, but on the combination of a Newton-Raphson method and the least-squares method. The proposed method has the quadratic convergence rate [16], because it is the quadratic term, not its coefficient that is the main factor of the convergence. The Jacobian matrix of the traditional Newton-Raphson method needs to be recalculated in each iteration, while the proposed modification only requires recalculation of some elements of its Jacobian matrix.…”

Section: Proposed Modification Of Newton-raphson Algorithm and Estimamentioning

confidence: 99%

“…The estimation process should be stopped in step when the condition is met

N^{()(, k + 1)} = N^{()(, k)}

Then the estimated value of the i th harmonic is defined as

g_{i}^{()(, k *)} ()(, t) = X_{i}^{()(, k *)} \cos ()(, i ω^{()(, k *)} t + ϕ_{i}^{()(, k *)})

where k * is the value of k for which the condition (38) is fulfilled, and

\begin{matrix} right leftthickmathspace.5em \\ X_{i}^{(k *)} & = \sqrt{{()(, A_{i}^{()(, k *)})}^{2} + {()(, B_{i}^{()(, k *)})}^{2}} \\ ϕ_{i}^{(k *)} & = - normalarctg \frac{B_{i}^{(k *)}}{A_{i}^{(k *)}} \end{matrix}

In the proposed algorithm for estimation of the unknown parameters of the processed power signal, an iterative scheme is not applied on the Newton–Raphson method, but on the combination of a Newton–Raphson method and the least‐squares method. The proposed method has the quadratic convergence rate [16], because it is the quadratic term, not its coefficient that is the main factor of the convergence. The Jacobian matrix of the traditional Newton–Raphson method needs to be recalculated in each iteration, while the proposed modification only requires recalculation of some elements of its Jacobian matrix.…”

Section: Proposed Algorithmmentioning

confidence: 99%

Computational effective modified Newton–Raphson algorithm for power harmonics parameters estimation

Petrovič¹,

Rozgić²

2018

IET signal process.

View full text Add to dashboard Cite

This study proposes a new algorithm for power harmonics parameters estimation based on the modified Newton-Raphson method. The main modification is achieved through reconfiguration of the Jacobian matrix and direct calculation of its characteristic coefficients without the necessity of inversion. The zero-crossing method was used to compute the frequency basically for initial frequency estimation. With additional digital filtering, the parameters can be initialised properly and the updating steps can be supervised for fast quadratic convergence of Newton-Raphson iterations. This combined approach yields high accuracy and good tracking speed, thereby significantly facilitating both the computation and programming. Reliability and effectiveness of the proposed method were confirmed through simulation tests and results. 2 Proposed algorithm Assume that the input signal of the fundamental frequency f is band limited to the first M harmonic components. This form of continuous signal with a complex harmonic content can be represented as a sum of the Fourier components as follows:

show abstract

On the Convergence of Inexact Newton Methods

Cited by 6 publications

References 13 publications

Globalization technique for projected Newton–Krylov methods

Globalization technique for projected Newton–Krylov methods

Fault Tolerant Control of PMSM Drive Using Luenberger and Adaptive Back-EMF Observers

Computational effective modified Newton–Raphson algorithm for power harmonics parameters estimation

Contact Info

Product

Resources

About