Nyström method - Wikipedia

Abstraction: Numerical quadrature approach to solving integral equations discretely

Key points:

• Replaces the integral in an integral equation with a weighted sum at representative quadrature points, converting the problem to a linear system
• Produces N equations in N unknowns, requiring O(N^3) operations to solve; high-order quadrature rules preferred to keep N small
• Applied directly to Fredholm equations of the second kind: y(x) = f(x) + integral of K(x,t)y(t) dt
• Gaussian quadrature is normally a good choice for smooth, non-singular kernels
• The discrete system may be ill-conditioned depending on the original problem and chosen quadrature rule

Connections: Numerical Methods · Integral Equations

Source: http://en.wikipedia.org/wiki/Nystr%C3%B6m_method