## Abstract

The aim of the present paper is to analyze the non-normality of the matrices (finite dimensional operators) which result when some Chebyshev-type methods are used in order to solve second order differential two-point boundary value problem.

We consider in turn the classical Chebyshev-tau method as well as two variants of the Chebyshev-Galerkin 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, i.e., non-normality ratio close to 0, exhibiting pure real spectrum, this measure remains the unique indicator of non-normality. In such cases the pseudospectrum tells nothing about non-normality.

## Authors

**Gheorghiu**

Tiberiu Popoviciu Institute of Numerical Analysis

## Keywords

Non-normal matrices; scalar measure; Chebyshev spectral approximation; two point boundary value problem.

### References

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## Cite this paper as

C.I. Gheorghiu, *On spectral properties of Chebyshev-type methods. Dimensions vs. structure*, Studia Univ. Babeş-Bolyai Math., **L **(2005) 61-66.

## About this paper

##### Publisher Name

Babes-Bolyai University

##### Paper on journal website

##### Print ISSN

0252-1938

##### Online ISSN

2065-961x

## MR

?

## ZBL

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## Google Scholar

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