Abstract
We know from the previous chapter that to calculate an intermediate eigenvalue λ of a large-size matrix A can be quite expensive. It often occurs that the matrix A depends continuously on a parameter x and consequently λ is a continuous function of x. Hence, it seems to be practical to calculate the function λ only for some values x and after that to connect—interpolate—smoothly in some way the obtained λ-values, using a method requiring significantly fewer operations. Then we have to be aware that the price of the decreased cost is the following: moving away from the exact values we obtain the value of λ(x) with an increasing error.
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© 2016 Springer International Publishing Switzerland
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Stoyan, G., Baran, A. (2016). Interpolation. In: Elementary Numerical Mathematics for Programmers and Engineers. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-44660-8_6
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DOI: https://doi.org/10.1007/978-3-319-44660-8_6
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-44659-2
Online ISBN: 978-3-319-44660-8
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