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Enhancing Rate of Convergence in GMRES Using Incomplete LU Factorizations

Kumlien, William LU (2024) In Bachelor’s Theses in Mathematical Sciences NUMK11 20241
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
In many fields of science, solving large sparse systems of linear equations is a critical task. Direct solvers often fall out favour due to their high computational costs and memory requirements. Iterative solvers alleviate this issue but run the risk of converging slower than satisfactory when the associated matrix is ill-conditioned and has poorly distributed eigenvalues. This work will focus on ways to transform such a system into a more favorable form, by applying a preconditioner. Among preconditioners, the incomplete LU factorization stands out as one of the most efficient and reliable techniques. The incomplete LU factorization is a cheap approximation of the LU decomposition that retains sparsity in the factors L and U. In this... (More)
In many fields of science, solving large sparse systems of linear equations is a critical task. Direct solvers often fall out favour due to their high computational costs and memory requirements. Iterative solvers alleviate this issue but run the risk of converging slower than satisfactory when the associated matrix is ill-conditioned and has poorly distributed eigenvalues. This work will focus on ways to transform such a system into a more favorable form, by applying a preconditioner. Among preconditioners, the incomplete LU factorization stands out as one of the most efficient and reliable techniques. The incomplete LU factorization is a cheap approximation of the LU decomposition that retains sparsity in the factors L and U. In this thesis, theory and practical guidelines for two types of incomplete LU factorizations will be provided, the ILU(0) and the ILUT. (Less)
Please use this url to cite or link to this publication:
author
Kumlien, William LU
supervisor
organization
course
NUMK11 20241
year
type
M2 - Bachelor Degree
subject
publication/series
Bachelor’s Theses in Mathematical Sciences
report number
LUNFNA-4058-2024
ISSN
1654-6229
other publication id
2024:K24
language
English
id
9177914
date added to LUP
2025-10-02 16:12:27
date last changed
2025-10-02 16:12:27
@misc{9177914,
  abstract     = {{In many fields of science, solving large sparse systems of linear equations is a critical task. Direct solvers often fall out favour due to their high computational costs and memory requirements. Iterative solvers alleviate this issue but run the risk of converging slower than satisfactory when the associated matrix is ill-conditioned and has poorly distributed eigenvalues. This work will focus on ways to transform such a system into a more favorable form, by applying a preconditioner. Among preconditioners, the incomplete LU factorization stands out as one of the most efficient and reliable techniques. The incomplete LU factorization is a cheap approximation of the LU decomposition that retains sparsity in the factors L and U. In this thesis, theory and practical guidelines for two types of incomplete LU factorizations will be provided, the ILU(0) and the ILUT.}},
  author       = {{Kumlien, William}},
  issn         = {{1654-6229}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Bachelor’s Theses in Mathematical Sciences}},
  title        = {{Enhancing Rate of Convergence in GMRES Using Incomplete LU Factorizations}},
  year         = {{2024}},
}