NP at TU München

Flashcards and summaries for NP at the TU München

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Study with flashcards and summaries for the course NP at the TU München

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:

wie heist erik

Select the correct answers:

  1. erik

  2. mztc

  3. pmoin

Exemplary flashcards for NP at the TU München on StudySmarter:

Designing computational methods for continuous problems mainly from linear
algebra (solving linear equation systems, finding eigenvalues etc.) and
calculus (finding roots or extrema etc.).

Select the correct answers:

  1. nein

  2. jwin

  3. ja

Exemplary flashcards for NP at the TU München on StudySmarter:

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

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?

Exemplary flashcards for NP at the TU München on StudySmarter:

What is dis?

Exemplary flashcards for NP at the TU München on StudySmarter:

What is the complexity of cubic spline interpolation?

Exemplary flashcards for NP at the TU München on StudySmarter:

What is the complexity of cubic spline interpolation?

Exemplary flashcards for NP at the TU München on StudySmarter:

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

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?

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:

Def. Interpolation

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Exemplary flashcards for NP at the TU München on StudySmarter:

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

wie heist erik

  1. erik

  2. mztc

  3. pmoin

NP

Designing computational methods for continuous problems mainly from linear
algebra (solving linear equation systems, finding eigenvalues etc.) and
calculus (finding roots or extrema etc.).

  1. nein

  2. jwin

  3. ja

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

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

What is dis?

Approc

NP

What is the complexity of cubic spline interpolation?

O(n)

NP

What is the complexity of cubic spline interpolation?

O(n)

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

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

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

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

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