摘要:

AbstractRecently, some new multilevel preconditioners for solving elliptic finite element discretizations by iterative methods have been proposed. They are based on appropriate splittings of the finite element spaces under consideration, and may be analyzed within the framework of additive Schwarz schemes. In this paper we discuss some multilevel methods for discretizations of the fourth‐order biharmonic problem by rectangular elements and derive optimal estimates for the condition numbers of the preconditioned linear systems. For the Bogner–Fox–Schmit rectangle, the generalization of the Bramble–Pasciak–Xu method is discussed. As a byproduct, an optimal multilevel preconditioner for nonconforming discretizations by Adini elements is als

ISSN:1070-5325    

DOI:10.1002/nla.1680020603

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe implicit Cholesky algorithm has been developed by several authors during the last 10 years but under different names. We identify the algorithm with a special version of Rutishauser's LR algorithm. Intermediate quantities in the transformation furnish several attractive approximations to the smallest singular value.The paper extols the advantages of using shifts with the algorithm. The nonorthogonal transformations improve accuracy.

ISSN:1070-5325    

DOI:10.1002/nla.1680020604

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractAn algorithm for pre‐ or post‐multiplication of a matrix by a plane rotation, using only three vector saxpy operations instead of the four vector operations usually considered necessary, is described. No auxiliary storage for overwriting is required. The method is shown to be numerically sta

ISSN:1070-5325    

DOI:10.1002/nla.1680020605

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:1070-5325    

DOI:10.1002/nla.1680020606

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:1070-5325    

DOI:10.1002/nla.1680020602

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY