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Investigation of Line Search Globalization and Scaling Aspects of Newton's Method in Two Industrial Implementations

el Gamal, Amira LU (2017) In Master's Theses in Mathematical Sciences NUMM11 20171
Mathematics (Faculty of Engineering)
Abstract
Simulating complex physical systems often requires solving systems of nonlinear algebraic equations. One of the most frequently used numerical methods to solve systems of nonlinear equations is Newton's method with its advantage of quadratic local convergence. However, Newton's method does not guarantee global convergence. This raises the need for combining Newton's method with a globalization strategy. One more problem that affects Newton's method convergence is caused by large differences in the scales of the iteration variables as well as the residuals. Although the Newton iteration is affine invariant, the termination criteria and norm calculations are not. This in turn affects the convergence. In this thesis, we address topics of... (More)
Simulating complex physical systems often requires solving systems of nonlinear algebraic equations. One of the most frequently used numerical methods to solve systems of nonlinear equations is Newton's method with its advantage of quadratic local convergence. However, Newton's method does not guarantee global convergence. This raises the need for combining Newton's method with a globalization strategy. One more problem that affects Newton's method convergence is caused by large differences in the scales of the iteration variables as well as the residuals. Although the Newton iteration is affine invariant, the termination criteria and norm calculations are not. This in turn affects the convergence. In this thesis, we address topics of Newton's method globalization using line search and the scaling of both variables and residuals from theoretical and implementation perspective. (Less)
Please use this url to cite or link to this publication:
author
el Gamal, Amira LU
supervisor
organization
course
NUMM11 20171
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Newton's Method, Line Search, Scaling, KINSOL
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFNA-3024-2017
ISSN
1404-6342
other publication id
2017:E65
language
English
id
8928333
date added to LUP
2017-11-27 14:32:46
date last changed
2017-11-27 14:32:46
@misc{8928333,
  abstract     = {Simulating complex physical systems often requires solving systems of nonlinear algebraic equations. One of the most frequently used numerical methods to solve systems of nonlinear equations is Newton's method with its advantage of quadratic local convergence. However, Newton's method does not guarantee global convergence. This raises the need for combining Newton's method with a globalization strategy. One more problem that affects Newton's method convergence is caused by large differences in the scales of the iteration variables as well as the residuals. Although the Newton iteration is affine invariant, the termination criteria and norm calculations are not. This in turn affects the convergence. In this thesis, we address topics of Newton's method globalization using line search and the scaling of both variables and residuals from theoretical and implementation perspective.},
  author       = {el Gamal, Amira},
  issn         = {1404-6342},
  keyword      = {Newton's Method,Line Search,Scaling,KINSOL},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {Investigation of Line Search Globalization and Scaling Aspects of Newton's Method in Two Industrial Implementations},
  year         = {2017},
}