| The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators |
| |
| 摘 要： | This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.
|
The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators |
| |
| Authors: | YiDu Yang and Zhen Chen |
| |
| Institution: | (1) School of Mathematics and Computer Sciences, Guizhou Normal University, Guiyang, 550001, China |
| |
| Abstract: | This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue. |
| |
| Keywords: | self-adjoint completely continuous operator spectral approximation the order-preserving convergence |
| 本文献已被 SpringerLink 等数据库收录！ |
