Nyström Method

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A Nyström Method is a numerical analysis method that ...



References

2019

  • (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Nyström_method Retrieved:2019-10-14.
    • In numerical analysis, the Nyström method or quadrature method seeks the numerical solution of an integral equation by replacing the integral with a representative weighted sum. The continuous problem is broken into [math]\displaystyle{ n }[/math] discrete intervals; quadrature or numerical integration determines the weights and locations of representative points for the integral.

      The problem becomes a system of linear equations with [math]\displaystyle{ n }[/math] equations and [math]\displaystyle{ n }[/math] unknowns, and the underlying function is implicitly represented by an interpolation using the chosen quadrature rule. This discrete problem may be ill-conditioned, depending on the original problem and the chosen quadrature rule.

      Since the linear equations require [math]\displaystyle{ O(n^3) }[/math] operations to solve, high-order quadrature rules perform better because low-order quadrature rules require large [math]\displaystyle{ n }[/math] for a given accuracy. Gaussian quadrature is normally a good choice for smooth, non-singular problems.

2014