NP at TU München

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What is the complexity of cubic spline interpolation?

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Def. Interpolation

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What is the difference between approximation and interpolation?
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What is the advantage of the scheme of Aitken and Neville over the Lagrange polynomials?

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Is the interpolant p that can be constructed using the scheme of Aitken and Neville identical to the sum of Lagrange polynomials for the same support points?

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Is polynomial interpolation with equidistant nodes a well-conditioned problem?

Exemplary flashcards for NP at the TU München on StudySmarter:

What is the complexity of cubic spline interpolation?
This was only a preview of our StudySmarter flashcards.
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Exemplary flashcards for NP at the TU München on StudySmarter:

What is the difference between approximation and interpolation?

Exemplary flashcards for NP at the TU München on StudySmarter:

What is the advantage of the scheme of Aitken and Neville over the Lagrange polynomials?

Exemplary flashcards for NP at the TU München on StudySmarter:

Is the interpolant p that can be constructed using the scheme of Aitken and Neville identical to the sum of Lagrange polynomials for the same support points?

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Is polynomial interpolation with equidistant nodes a well-conditioned problem?
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Was sind die Maschinenzahlen?

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Exemplary flashcards for NP at the TU München on StudySmarter:

NP

What is the complexity of cubic spline interpolation?
O(n)

NP

Def. Interpolation
Spezialfall der Approximation: die Werte der Funktion und der Interpolanten müssen an bestimmten Stellen gleich sein.

NP

What is the difference between approximation and interpolation?
Interpolation is a special case of approximation: If the function f and the approximant p have to be equal at certain points, the approximant becomes an interpolant.

NP

What is the advantage of the scheme of Aitken and Neville over the Lagrange polynomials?
The scheme of Aitken and Neville can evaluate p(x) at an intermediate point without an explicit formulation of p.

NP

Is the interpolant p that can be constructed using the scheme of Aitken and Neville identical to the sum of Lagrange polynomials for the same support points?
Yes, because of the uniqueness of the interpolation problem.

NP

Is polynomial interpolation with equidistant nodes a well-conditioned problem?
No, for large (7 or 8 and up), polynomial interpolation with equidistant nodes is extremely ill-conditioned.

NP

What is the complexity of cubic spline interpolation?
O(n)

NP

What is the difference between approximation and interpolation?
Interpolation is a special case of approximation: If the function f and the approximant p have to be equal at certain points, the approximant becomes an interpolant.

NP

What is the advantage of the scheme of Aitken and Neville over the Lagrange polynomials?
The scheme of Aitken and Neville can evaluate p(x) at an intermediate point without an explicit formulation of p.

NP

Is the interpolant p that can be constructed using the scheme of Aitken and Neville identical to the sum of Lagrange polynomials for the same support points?
Yes, because of the uniqueness of the interpolation problem.

NP

Is polynomial interpolation with equidistant nodes a well-conditioned problem?
No, for large (7 or 8 and up), polynomial interpolation with equidistant nodes is extremely ill-conditioned.

NP

Was sind die Maschinenzahlen?
Die endliche Menge M der in einem Rechner darstellbaren Zahlen

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NPK 2 at

Universität Kassel

NT at

Universität Giessen

NpD Marie at

Helmut-Schmidt-Universität/ Universität der Bundeswehr

NS at

Fachhochschule des bfi Wien

NPM at

Pädagogische Hochschule Ludwigsburg

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