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By B. Sz.-Nagy

Appendix to Frigyes Riesz and Bela Sz.-Nagy, useful research: Extensions of Linear differences in Hilbert area Which expand past This house

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2) . I shall show them . 1. The method of combination of solutions leads to a non suitabid process. 2) i s combination. 2. =b = 0 of the . The results determined by . We obtained 1 1,2 a suitable x - (500 + solve the initial problem 4th order for The factorization methods leads to By this method cos ini- step h = 0,025 a r e given in Table a suitable process. g. (12) ) we solve the following system Let us solve the same problem a s in Example 3 . 1 by this method. The initial problems a r e also h = 0,025 .

1 of these disturbances a r e admissible. It i s obvious that the questions of existence of a suitable numerical process for the solution of the given problem i s very important. The method of factorization may be generalized to a general boundary ( o r multipoint) problem for the system x'(s) J. Taufer , s e e - A(s) x (x) (38), (39) , has = f(s). 4). See (3) . In (7) and (12) the stability of the differential equations of the factorization method in special c a s e s has been studied. 3 As an example I shall show the computation of a continuous beam of 20 fields built in at the end and constantly loaded.

The e r r o r bounds for the trapezoid formula a r e studied in many papers. See (4) (5), (21), (24)/ and others. We will now analyse the proF blem of the choice of the quadrature formula according to the information we mentioned previously. In our considerations we shall confine the class of possible formulae to the linear one, The choice of the quadrature formula means, in our case, to determine of the sequence of linear functionals I in the form n with the requirement that Jn(f) + J(f) (weak) for all functions f(x) of the given class of functions.

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Appendix to Frigyes Riesz and Bela Sz.-Nagy Functional Analysis by B. Sz.-Nagy

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