Investigation of Line Search Globalization and Scaling Aspects of Newton's Method in Two Industrial Implementations
(2017) In Master's Theses in Mathematical Sciences NUMM11 20171Mathematics (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:
http://lup.lub.lu.se/studentpapers/record/8928333
 author
 el Gamal, Amira ^{LU}
 supervisor

 Claus Führer ^{LU}
 organization
 course
 NUMM11 20171
 year
 2017
 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
 LUNFNA30242017
 ISSN
 14046342
 other publication id
 2017:E65
 language
 English
 id
 8928333
 date added to LUP
 20171127 14:32:46
 date last changed
 20171127 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 = {14046342}, 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}, }