Linear Equations for Coefficients

• Our condition becomes

  

  (linear nature of integral ensures that (NI.4) guarantees exactness of (NI.2) for all polynomials of degree ).

• We can write (NI.4) as:

  

  is column vector of 's, is column vector of 's and A is matrix of coefficients . It is easy to show that A is nonsingular (if distinct) and hence that (NI.5) can be solved and (NI.2) established for any in (NI.1).

• Usually (NI.5) is solved---once and for all for given ---and then (NI.2) can be used quickly for any that crops up.

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