Conjugate Gradient Method for Rank Deficient Saddle Point Problems

We propose an alternative iterative method to solve rank deficient problems arising in many real applications such as the finite element approximation to the Stokes equation and computational genetics. Our main contribution is to transform the rank deficient problem into a smaller full rank problem,...

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Bibliographic Details
Published inNumerical algorithms Vol. 35; no. 2-4; pp. 139 - 154
Main Authors Wu, X., Silva, B.P.B., Yuan, J.Y.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.04.2004
Subjects
Conjugate gradient method
Iterative methods
Mathematical analysis
Saddle points
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Summary:We propose an alternative iterative method to solve rank deficient problems arising in many real applications such as the finite element approximation to the Stokes equation and computational genetics. Our main contribution is to transform the rank deficient problem into a smaller full rank problem, with structure as sparse as possible. The new system improves the condition number greatly. Numerical experiments suggest that the new iterative method works very well for large sparse rank deficient saddle point problems.
ISSN:1017-1398
1572-9265
DOI:10.1023/B:NUMA.0000021758.65113.f5