UM Math Graduate Student Seminar

Ondrej Zjevik
University of Miami

will present

Numerical Quadrature

Friday, April 8, 2016, 5:00pm
Ungar Building Room 402


Abstract:

In modern terminology the term “quadrature” represents the numerical evaluation of a definite integral. It is well documented that Archimedes of Syracuse (287 BC – 212 BC) derived formulas for the surface area and volume of a sphere, and the area under a parabola. In this talk, we will focus on the modern development of numerical integration based on different interpolation methods. We will derive and compare the Newton—Cotes formulas and Gaussian quadrature formulas. Extending these formulas for multidimensional integrals is possible due to the Fubini’s theorem, but the computational complexity grows exponentially. We will discuss two methods that avoid this phenomenon.

 


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