gs.mma

Mathematical Methods by Moor n Stiling.

(* A Gram-Schmidt procedure *)
(* Copyright 1999 by Todd K. Moon *)

gs[p_,a_,b_,w_,t_] :=
(* p = list of input functions
   a = lower limit of integration
   b = upper limit of integration
   w = weight function
   t = variable of integration
*)
  Module[{i,j,k,q,ek,n1},  (* q = list of output functions *)
   Nfunc = Length[p];
   q = {};
   (* find the first non-null function *)
   For[k= 1, k <= Nfunc, k++,
      n1 = Integrate[ p[[k]]^2 w,{t,a,b}];
      If[n1 != 0, Break[]];
   ];
   If[k>Nfunc,
      Return[q];
   ];
   j = 1;
   q = Append[q,p[[k]]/Sqrt[n1]];
   (* Now do the rest of them *)
   For[  , k <= Nfunc, k++,
      ek = p[[k]] - Sum[ Integrate[p[[k]] q[[i]] w,{t,a,b}] q[[i]],{i,1,j}];
      n1 = Integrate[ek^2 w,{t,a,b}];  (* find the norm *)
      If[n1 != 0,     (* if not dependent on the others *)
         ++j;         (* add it to the list *) 
         q = Append[q,ek/Sqrt[n1]];
      ];
   ];
   q   (* return value *)
]