scholarly journals An iterative method to compute Moore-Penrose inverse based on gradient maximal convergence rate

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1269-1276 ◽  
Author(s):  
Xingping Sheng ◽  
Tao Wang
Keyword(s):  
Convergence Rate ◽  
Iterative Method ◽  
Computation Time ◽  
The Other ◽  
Singular Matrix ◽  
Initial Matrix ◽  
Numerical Example

In this paper, we present an iterative method based on gradient maximal convergence rate to compute Moore-Penrose inverse A+ of a given matrix A. By this iterative method, when taken the initial matrix X0 = A*, the M-P inverse A+ can be obtained with maximal convergence rate in absence of round off errors. In the end, a numerical example is given to illustrate the effectiveness, accuracy and its computation time, which are all superior than the other methods for the large singular matrix.

scholarly journals An iterative algorithm to compute the Bott-Duffin inverse and generalized Bott-Duffin inverse

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 769-776 ◽  
Author(s):  
Xingping Sheng
Keyword(s):  
Iterative Method ◽  
Finite Number ◽  
Iterative Algorithm ◽  
Inner Product ◽  
Initial Matrix ◽  
Orthogonal Projector ◽  
Numerical Example ◽  
Roundoff Errors ◽  
Number Of Iterations ◽  
Finite Number Of Iterations

Let L be a subspace of Cn and PL be the orthogonal projector of Cn onto L. For A?Cn?n, the generalized Bott-Duffin (B-D) inverse A(+)(L) is given by A(+)(L)= PL(APL + PL?)?. In this paper, by defined a non-standard inner product, a finite formulae is presented to compute Bott-Duffin inverse A(?)(L) = PL(APL+P?)? and generalized Bott-Duffin inverse A(?)(L)= PL (APL+PL?)? under the condition A is L?zero (i.e., AL?L?={0}). By this iterative method, when taken the initial matrix X0 = PLA?PL, the Bott-Duffin inverse A(?1)(L) and generalized Bott-duffin inverse A(?)(L) can be obtained within a finite number of iterations in absence of roundoff errors. Finally a given numerical example illustrates that the iterative algorithm dose converge.

Comparison Results on Preconditioned AOR-Type Iterative Method for M-Matrices

2013 ◽  
Vol 756-759 ◽  
pp. 2629-2633
Author(s):  
Ting Zhou ◽  
Hong Fang Cui
Keyword(s):  
Linear System ◽  
Convergence Rate ◽  
Iterative Method ◽  
Iterative Methods ◽  
Science And Engineering ◽  
Numerical Example ◽  
Comparison Results ◽  
Preconditioned Iterative ◽  
Preconditioned Iterative Methods

For solving the linear system, different preconditioned iterative methods have been proposed by many authors. M-matrices appear in many areas of science and engineering. In this paper, we present preconditioned AOR-type iterative method and the SOR-type iterative method with a preconditioner for solving the M-matrices. In addition, the relation between the convergence rate of preconditioned AOR-type iterative method and the parameters are brought to light. Finally, a numerical example is also given to illustrate the results.

scholarly journals Two Identification Methods for Dual-Rate Sampled-Data Nonlinear Output-Error Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Chen ◽  
Ruifeng Ding
Keyword(s):  
Stochastic Gradient ◽  
The Other ◽  
Identification Algorithm ◽  
Sampled Data ◽  
Unknown Parameters ◽  
Auxiliary Model ◽  
Identification Methods ◽  
Numerical Example ◽  
Output Error ◽  
Polynomial Transformation

This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods.

scholarly journals A Modification of Minimal Residual Iterative Method to Solve Linear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Xingping Sheng ◽  
Youfeng Su ◽  
Guoliang Chen
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Linear Systems ◽  
Residual Error ◽  
Projection Technique ◽  
Numerical Example ◽  
Minimal Residual

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear systemAx=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.

scholarly journals Parallel computing applied to auto-tuning of state feedback speed controller for PMSM drive

2019 ◽  
Vol 28 ◽  
pp. 01031
Author(s):  
Rafal Szczepanski ◽  
Tomasz Tarczewski ◽  
Lech M. Grzesiak
Keyword(s):  
Parallel Computing ◽  
State Feedback ◽  
Computation Time ◽  
The Other ◽  
Speed Controller ◽  
Speed Up ◽  
Tuning Process ◽  
Auto Tuning ◽  
Reduce Computation Time ◽  
Simulation Time

Nowadays the simulation is inseparable part of researcher's work. Its computation time may significantly exceed the experiment time. On the other hand, multi-core processors can be used to reduce computation time by using parallel computing. The parallel computing can be employed to decrease the overall simulation time. In this paper the parallel computing is used to speed-up the auto-tuning process of state feedback speed controller for PMSM drive.

scholarly journals Jump or kink: on super-efficiency in segmented linear regression breakpoint estimation

Biometrika ◽  
2020 ◽  
Author(s):  
Yining Chen
Keyword(s):  
Structural Change ◽  
Linear Regression ◽  
Convergence Rate ◽  
Pointwise Convergence ◽  
Mean Absolute Error ◽  
Absolute Error ◽  
The Other ◽  
Fixed Parameter ◽  
The Mean ◽  
Potential Remedy

Summary We consider the problem of segmented linear regression with a single breakpoint, with the focus on estimating the location of the breakpoint. If $n$ is the sample size, we show that the global minimax convergence rate for this problem in terms of the mean absolute error is $O(n^{-1/3})$. On the other hand, we demonstrate the construction of a super-efficient estimator that achieves the pointwise convergence rate of either $O(n^{-1})$ or $O(n^{-1/2})$ for every fixed parameter value, depending on whether the structural change is a jump or a kink. The implications of this example and a potential remedy are discussed.

Determine to Slip Surface in Waterfront Soil Slope Analysis

2011 ◽  
Vol 378-379 ◽  
pp. 466-469 ◽  
Author(s):  
Jun Jie Wang ◽  
Hui Ping Zhang ◽  
Tao Liu
Keyword(s):  
Iterative Method ◽  
Slip Surface ◽  
The Other ◽  
New Method ◽  
Soil Slope ◽  
Balance Equations ◽  
Inclined Plane ◽  
Slope Analysis ◽  
Basic Assumptions ◽  
Straight Lines

This study focuses on the method to determine the slip surface in waterfront soil slope analysis under static and seismic conditions. Based on the limiting equilibrium theory and the stress analyzing method, a new method to determine the slip surface is suggested. In the method, the two basic assumptions are considered in order to solve the problem. One is that the slip surface comprises a series of straight lines, and the other is that the interslice boundary is an inclined plane. Three balance equations for any slice are proposed. The iterative method to solve the balance equations is also suggested. In the new method, the slip surface is obtained slice by slice going from downhill to uphill in terms of the balance equations of the slice, not predefined.

Study of the Effect of Boundary Conditions on Residual Stresses in Welding Using Element Birth and Element Movement Techniques

2003 ◽  
Author(s):  
Ihab F. Z. Fanous ◽  
Maher Y. A. Younan ◽  
Abdalla S. Wifi
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Boundary Conditions ◽  
Welding Process ◽  
Computation Time ◽  
3D Models ◽  
The Other ◽  
3D Analysis ◽  
The Media ◽  
Element Movement

The structure in which the welding process is performed highly affects the residual stresses generated in the welding. This effect is simulated by choosing the appropriate boundary conditions in modeling the welding process. The major parameters of the boundary conditions are the method by which the base metal is being fixed and the amount of heat being applied through the torch. Other parameters may include the coefficients of thermal heat loss from the plate which may simulate the media in which the welding is taking place. In modeling the welding process, 2D forms of approximation were developed in analyzing most of the models of such problem. 3D models analyzing the welding process were developed in limited applications due to its high computation time and cost. With the development of new finite element tools, namely the element movement technique developed by the authors, full 3D analysis of the welding process is becoming in hand. In the present work, three different boundary conditions shall be modeled companng their effect on the welding. These boundary conditions shall be applied to two models of the welding process: one using the element birth technique and the other using the element movement technique showing the similarity in their responses verifying the effectiveness of the latter being accomplished in a shorter time.

Kinematics of a n–bay triangle–triangle variable geometry truss manipulator

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 263-267
Author(s):  
L. Beiner
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Variable Length ◽  
Variable Geometry ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Forward And Inverse Kinematics ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

SUMMARYVariable geometry truss manipulators (VGTM) are static trusses where the lengths of some members can be varied, allowing one to control the position of the free end relative to the fixed one. This paper deals with a planar VGTM consisting of a n–bay triangle-triangle truss with one variable length link (i.e. one DOF) per bay. Closed-form solutions to the forward, inverse, and velocity kinematics of a 3-DOF version of this VGTM are presented, while the forward and inverse kinematics of an n–DOF (redundant) one are solved by a recursive and an iterative method, respectively. A numerical example is presented.

A fast procedure for computing incremental growth distances

Robotica ◽  
2000 ◽  
Vol 18 (4) ◽  
pp. 429-441 ◽  
Author(s):  
Sun-Mog Hong ◽  
Joon-Hyuek Yeo ◽  
Hae-Wook Park
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Computation Time ◽  
Interference Detection ◽  
Geometric Complexity ◽  
Numerical Example ◽  
Incremental Growth ◽  
Fast Procedure ◽  
Three Dimensional Space

A fast numerical procedure is presented for computing growth distances between a pair of polytopes in three dimensional space that move incrementally along specified smooth paths. The procedure carrys out the growth distance evaluations efficiently by predicting and verifying contact configurations between a pair of grown polytopes. In the prediction and verification the procedure uses vertex and facial characterizations of polytopes and exploits their geometric adjacency information. The computation time, in average, is very small and does not depend significantly on the geometric complexity of two polytopes. A numerical example is presented to demonstrate the applicability of the procedure to interference detection in robotic simulations.

Sign in / Sign up

Export Citation Format

Share Document