Introduction to Numerical Integration

• The problem of finding is closely related to both differentiation rules and to formulae for expanding in . If the expansion functions are nice, we can plug in expansion for f and do term by term integral. It divides into

• NI.1,2: assumed known at prescribed points (cf. Lagrange interpolation)

• NI.3: We can choose points where to be calculated (cf. Chebyshev expansion for interpolation)

• NI.5: Monte Carlo Integration

• NI.5: is most important as it is what you get in big problems with multidimensional integrals!

• NI.4: has remarks on use of parallel computers.

  A good compendium of rules will be found in M. Abramowitz and J. Stegun, ``Handbook of Mathematical Functions.''

Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu