Numerical safeguarded use of the implicit restarted Lanczos algorithm for solving nonlinear eigenvalue problems and its monotonicity analysis

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dc.contributor.advisorSorensen, Danny C.en_US
dc.creatorAbdel-Aziz, Mohammedi Radwan Hassanen_US
dc.date.accessioned2009-06-04T00:27:26Zen_US
dc.date.available2009-06-04T00:27:26Zen_US
dc.date.issued1993en_US
dc.description.abstractIn this thesis, we develop an efficient accurate numerical algorithm for evaluating a few of the smallest eigenvalues and their corresponding eigenvectors for large scale nonlinear eigenproblems. The entries of the matrices in these problems are transcendental functions approximated well by rational functions. This algorithm is based upon the Implicit Restarted Lanczos method for solving the linear eigenvalue sub-problems that arise in conjunction with a new zero-finding technique that uses rational function interpolation to approximate the generalized eigenvalues. We have tested this technique on high performance computers and we present some numerical experiments that demonstrate the efficiency and the accuracy of this procedure. Our monotonicity analysis theory shows that the parameterized eigenvalue curves (monotone increasing) are much better behaved than the parameterized determinant curves that have erratic behavior. Our numerical and monotonicity analyses are sufficiently general that they hold for any problem having monotone increasing generalized eigenvalues. This type of problem is associated with the mixed finite element formulation that involves a frequency independent stiffness and frequency dependent mass matrices.en_US
dc.format.extent104 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoThesis Math.Sci. 1993 Abdel-Azizen_US
dc.identifier.citationAbdel-Aziz, Mohammedi Radwan Hassan. "Numerical safeguarded use of the implicit restarted Lanczos algorithm for solving nonlinear eigenvalue problems and its monotonicity analysis." (1993) Diss., Rice University. <a href="https://hdl.handle.net/1911/16596">https://hdl.handle.net/1911/16596</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/16596en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.subjectComputer scienceen_US
dc.subjectApplied mechanicsen_US
dc.titleNumerical safeguarded use of the implicit restarted Lanczos algorithm for solving nonlinear eigenvalue problems and its monotonicity analysisen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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