Article ID: | iaor19931513 |
Country: | United States |
Volume: | 34 |
Issue: | 4 |
Start Page Number: | 581 |
End Page Number: | 613 |
Publication Date: | Dec 1992 |
Journal: | SIAM Math Rev |
Authors: | Xu Jinchao |
Keywords: | programming: nonlinear |
The main purpose of this paper is to give a systematic introduction to a number of iterative methods for symmetric positive definite problems. Based on results and ideas from various existing works on iterative methods, a unified theory for a diverse group of iterative algorithms, such as Jacobi and Gauss-Seidel iterations, diagonal preconditioning, domain decomposition methods, multigrid methods, multilevel nodal basis preconditioners and hierarchical basis methods, is presented. By using the notions of space decomposition and subspace correction, all these algorithms are classified into two groups, namely