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    STUDIA MATHEMATICA - Issue no. 1 / 2005  
         
  Article:   ON SPECTRAL PROPERTIES OF SOME CHEBYSHEV-TYPE METHODS DIMENSION VS. STRUCTURE.

Authors:  CĂLIN-IOAN GHEORGHIU. 		 
       
         
  Abstract:  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.  
         
     
         
         
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