György Bicsák, Dávid Sziroczák, Aaron Latty

Numerical methods


Spline Interpolation [3]

Up to this point, to interpolate n+1 points, a n-th degree polynomial has been used. For example, to interpolate 11 input points, by using the Lagrange interpolation we got an 10th degree polynomial, which is not really practical, furthermore is really ugly. This means, that the former interpolation methods work well only for a low number of points, but for 101 or 1001 input points, it is not a good solution to use an 100th or 1000th degree polynomial, it would not make much sense. Additionally, considering 11 points and the 10th degree polynomial, due to the peaks, generated by the high degree polynomial, the interpolation method can make significant errors, as it can be seen in Figure 17. This means, the higher the number of initial points the higher degree polynomial is required, thus the error of the interpolation method is also higher.

Numerical methods

Tartalomjegyzék


Kiadó: Akadémiai Kiadó

Online megjelenés éve: 2019

ISBN: 978 963 454 283 4

This book on Numerical Methods is part of the Transportation and Vehicle Engineering Faculty’s curriculum at the Budapest University of Technology and Economics, created under the Stipendium Hungaricum Scholarship Programme. The book demonstrates the aim of developing and using numerical methods. Instead of relying on more complicated and expensive analytical solution methods, simpler arithmetical equations are used to approximate the accurate solution with the required level of accuracy. After discussing the various sources and propagation of solution errors, the book discusses the solution of single variable equations and system of equations. Following chapters describe the two main curve fitting methods; approximation and interpolation. These chapters are followed by the numerical differentiation and integration methods, then finally the numerical solutions for ordinary and partial differentiation equations are outlined. MATLAB is one of the most popular choice today for numerical computing, with its user friendly, yet powerful computing capability. It is practically an industry standard for prototyping and new developments, and there is great value for students to be introduced to solving problems with MATLAB. Many chapters in the notes show examples implemented in MATLAB, with actual working code available to use and practice.

Hivatkozás: https://mersz.hu/bicsak-numerical-methods//

BibTeXEndNoteMendeleyZotero

Kivonat
fullscreenclose
printsave