zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Accuracy and speed in computing the Chebyshev collocation derivative. (English) Zbl 0840.65010

The authors discuss Chebyshev collocation methods and study several algorithms for computing Chebyshev spectral derivatives. Then they describe a preconditioning method for reducing the roundoff error. By means of a statistical approach they estimate the minimum possible roundoff error.

Using different algorithms they obtain some results on the accuracy of computing. The numerical errors associated with computing the elements of the differentiation matrix are described. They find out that if the entries of the matrix are computed accurately, then the roundoff error of the matrix-vector multiplication is as small as that obtained by the transform-recursion algorithm. For most practical grid sizes used in computations, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.

65D25Numerical differentiation
65N35Spectral, collocation and related methods (BVP of PDE)
65Y20Complexity and performance of numerical algorithms
65F30Other matrix algorithms
65G50Roundoff error