AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA MATHEMATICA - Ediţia nr.1 din 2005 | |||||||
Articol: |
ON SPECTRAL PROPERTIES OF SOME CHEBYSHEV-TYPE METHODS DIMENSION VS. STRUCTURE. Autori: CĂLIN-IOAN GHEORGHIU. |
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Rezumat: The aim of the present paper is to analyze the non-normalty of the matrices (finite dimensional operators) which result when some hebyshev-type methods are used in order to solve second order differential two-point boundary value problems. We consider in turn the classical hebyshev-tau method as well as two variants of the hebyshev-Galerki method. As measure of non-normality we use the non-normality ratio introduced in a previous paper. The competition between the dimension of matrices (the order of approximation) and their structure (the numerical method itself) with respect to normality is the core of our study. It is observed that for quasi normal matrices, ie., non-normality ratio close to 0, exhibiting pure real spectrum, this measure remains the unique indicator of non-normalty. In such cases the pseudospectrum tels nothing about non-normality. | |||||||