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B U , 11 ni ?* n. The standard method of constructing orthonormal functions, while completely satisfying logically, has certain practical disadvantages. For example, if the integrations must be done numerically (as would be necessary if either the ƒ»• or the boundary of R were complicated functions, or if the ƒ* were tabular functions) then the mere tabulation of the intermediate functions which appear becomes burdensome. One would prefer to perform the necessary integrations on the original functions ƒ»• and then proceed by a purely algebraic or numerical proces3 to obtain the gi. This can be done. If we let Ni be the numerator and Di the denominator of the orthonormal function gi, and if we put Fij—fitfiJjdR, then the standard orthonormalization process can be shown, by simple algebra, to result in the following:

Simplified technique for constructing orthonormal functions