Numerical methodsLesson 1 of 3 in the course Interpolation

Interpolation: Methods, Error, and Applications

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Interpolation is a way to estimate values between known data points. It is widely used when measurements or samples are available only at particular inputs, but an estimate is needed at an intermediate input.

Suppose a function has been sampled at a finite set of inputs. The resulting data points provide known pairs such as (xa,ya)(x_a,y_a) and (xb,yb)(x_b,y_b). Interpolation constructs an estimate at an input between known inputs, using the available data.

All flashcards

Interpolation
Constructing estimates from known data points, usually at inputs within their range.
Polynomial interpolation
For n distinct data points, the unique interpolating polynomial has degree at most n − 1.
Spline interpolation
A method that joins low-degree polynomial pieces smoothly across intervals.
Kriging
The name used in geostatistics for Gaussian process regression.
Inverse distance weighting
A spatial method that gives closer data points greater influence on an estimate.

Quiz questions

  1. How many distinct polynomials of degree at most n − 1 interpolate n distinct data points?Answer: Exactly one.
  2. In the exponential interpolation formula over [0, b], what role does k play?Answer: It controls the shape of the transition between endpoint values.
  3. What conditions characterize a natural cubic spline?Answer: It is twice continuously differentiable, with zero second derivative at both range endpoints.
  4. In inverse distance weighting, what is the effect of increasing the inverse power?Answer: Nearby points exert more influence relative to distant points.
  5. How does extrapolation differ from interpolation?Answer: Extrapolation estimates values outside the range of known inputs.

Based on the Wikipedia article Interpolation, licensed CC BY-SA 4.0. Adapted into a summary, flashcards and quizzes.

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