Numerisches Programmieren at TU München

Flashcards and summaries for Numerisches Programmieren at the TU München

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Study with flashcards and summaries for the course Numerisches Programmieren at the TU München

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

Is numeric quadrature the best method for computing the integral?

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

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

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

What is the complexity of cubic spline interpolation?

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

Vor- und Nachteile der fixed point arithmetic

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

Ziele für einen numerischen Algorithmus

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

Def. Interpolation

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

Wofür wird numerische Quadratur verwendet?

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

What is the difference between approximation and interpolation?

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

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

Exemplary flashcards for Numerisches Programmieren 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 Numerisches Programmieren at the TU München on StudySmarter:

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

Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

What is the complexity of cubic spline interpolation?

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Exemplary flashcards for Numerisches Programmieren at the TU München on StudySmarter:

Numerisches Programmieren

Is numeric quadrature the best method for computing the integral?

No, it should only be used when all other mehtods (such as closed integration using substitution, partial integration etc.) fail.

Numerisches Programmieren

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.

Numerisches Programmieren

What is the complexity of cubic spline interpolation?

O(n)

Numerisches Programmieren

Vor- und Nachteile der fixed point arithmetic
Vorteile:
– kann rationale Zahlen darstellen
Nachteile:
– begrenzter Zahlenbereich, oft kommt es zu Overflows
– zwischen z.B. 0 und 0,001 braucht man oft zusätzliche Zahlen, während zwischen z.B. 998,999 und 999 eine grobere Aufteilung ausreichend wäre

Numerisches Programmieren

Ziele für einen numerischen Algorithmus
– kleiner Diskretisierungsfehler
– kleiner Rundungsfehler
– Effinzienz: minimale Laufzeit

Numerisches Programmieren

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

Numerisches Programmieren

Wofür wird numerische Quadratur verwendet?
Zur numerischen Berechnung bestimmter Integrale.

Numerisches Programmieren

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.

Numerisches Programmieren

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.

Numerisches Programmieren

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.

Numerisches Programmieren

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.

Numerisches Programmieren

What is the complexity of cubic spline interpolation?

O(n)

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