Path-following methods for Kuhn-Tucker curves by an active index set strategy

2006 ◽  
pp. 111-131 ◽  
Author(s):  
H. Gfrerer ◽  
Hj. Wacker ◽  
W. Zulehner ◽  
J. Guddat
Keyword(s):  
Path Following ◽  
Index Set ◽  
Active Index Set ◽  
Path Following Methods

Path-Following Methods for Linear Programming

SIAM Review ◽  
1992 ◽  
Vol 34 (2) ◽  
pp. 167-224 ◽  
Author(s):  
Clovis C. Gonzaga
Keyword(s):  
Linear Programming ◽  
Path Following ◽  
Path Following Methods

A Comparative Study of Parking Path Following Methods for Autonomous Parking System

2020 ◽  
Vol 15 (2) ◽  
pp. 147-159
Author(s):  
Minsung Kim ◽  
◽  
Gyubeom Im ◽  
Jaeheung Park
Keyword(s):  
Comparative Study ◽  
Path Following ◽  
Parking System ◽  
Path Following Methods

scholarly journals Path following methods for steady laminar Bingham flow in cylindrical pipes

2008 ◽  
Vol 43 (1) ◽  
pp. 81-117 ◽  
Author(s):  
Juan Carlos De Los Reyes ◽  
Sergio González
Keyword(s):  
Path Following ◽  
Bingham Flow ◽  
Path Following Methods ◽  
Steady Laminar

scholarly journals Path-Following Methods for Calculating Linear Surface Wave Dispersion Relations on Vertical Shear Flows

Water Waves ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 381-414 ◽  
Author(s):  
Peter Maxwell ◽  
Simen Å. Ellingsen
Keyword(s):  
Dispersion Relation ◽  
Wave Vector ◽  
Path Following ◽  
Wave Dispersion ◽  
Vertical Shear ◽  
Companion Matrix ◽  
Surface Boundary ◽  
Setup Cost ◽  
Surface Wave Dispersion ◽  
Path Following Methods

Abstract The path-following scheme in Loisel and Maxwell (SIAM J Matrix Anal Appl 39(4):1726–1749, 2018) is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current. This is equivalent to solving the Rayleigh stability equation with linearized free-surface boundary condition for each sought point on the curve. Taking advantage of the analyticity of the dispersion relation, a path-following or continuation approach is adopted. The problem is discretized using a collocation scheme, parametrized along either a radial or angular path in the wave vector plane, and differentiated to yield a system of ODEs. After an initial eigenproblem solve using QZ decomposition, numerical integration proceeds along the curve using linear solves as the Runge–Kutta $$F(\cdot )$$ F ( · ) function; thus, many QZ decompositions on a size 2N companion matrix are exchanged for one QZ decomposition and a small number of linear solves on a size N matrix. A piecewise interpolant provides dense output. The integration represents a nominal setup cost whereafter very many points can be computed at negligible cost whilst preserving high accuracy. Furthermore, a two-dimensional interpolant suitable for scattered data query points in the wave vector plane is described. Finally, a comparison is made with existing numerical methods for this problem, revealing that the path-following scheme is the most competitive algorithm for this problem whenever calculating more than circa 1,000 data points or relative normwise accuracy better than $$10^{-4}$$ 10 - 4 is sought.

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