The conditioning of FD matrix sequences coming from semi-elliptic differential equations
| Autor: | D. Noutsos, S. Serra Capizzano, P. Vassalos |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
spectral distribution
Dirichlet problem Finite differences Numerical Analysis boundary value problenis Algebra and Number Theory finite differences block toeplitz matrices Differential equation Mathematical analysis Boundary value problems Spectral distribution Toeplitz matrices Differential operator toeplitz matrices Elliptic operator Matrix (mathematics) Bounded function Discrete Mathematics and Combinatorics Geometry and Topology Connection (algebraic framework) Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Linear Algebra and its Applications. 428(2-3):600-624 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2007.08.008 |
| Popis: | In this paper we are concerned with the study of spectral properties of the sequence of matrices { A n ( a ) } coming from the discretization, using centered finite differences of minimal order, of elliptic (or semielliptic) differential operators L ( a , u ) of the form (1) - d d x a ( x ) d d x u ( x ) = f ( x ) on Ω = ( 0 , 1 ) , Dirichlet B.C. on ∂ Ω , where the nonnegative, bounded coefficient function a ( x ) of the differential operator may have some isolated zeros in Ω ¯ = Ω ∪ ∂ Ω . More precisely, we state and prove the explicit form of the inverse of { A n ( a ) } and some formulas concerning the relations between the orders of zeros of a ( x ) and the asymptotic behavior of the minimal eigenvalue (condition number) of the related matrices. As a conclusion, and in connection with our theoretical findings, first we extend the analysis to higher order (semi-elliptic) differential operators, and then we present various numerical experiments, showing that similar results must hold true in 2D as well. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect