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)
Higher order pseudospectral differentiation matrices. (English) Zbl 1086.65016

“We approximate the derivatives of a function f(x) by interpolating the function with a polynomial at the Chebyshev extrema nodes x k , differentiating the polynomial, and then evaluating the polynomial at the same nodes.”

The paper investigates the roundoff properties of various ways of setting up the matrix that maps the vector f ( x k ) to the vector of p-th derivatives f (p) (x k ) for arbitrary p. Simple numerical tests are reported.

Mostly, the paper is clearly written. But it would have been useful to explain the context in which this way of approximating derivatives is valuable. There is a vast difference between using such formulas in explicit approximation of derivatives of a given function (for which very poor results should be expected even in exact arithmetic) and using them as part of an implicit process like solving a differential equation.

65D25Numerical differentiation