A mean value theorem for linear functionals

Author:
D. Meek

Journal:
Math. Comp. **35** (1980), 797-802

MSC:
Primary 41A58; Secondary 65G99

DOI:
https://doi.org/10.1090/S0025-5718-1980-0572857-0

MathSciNet review:
572857

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: When working out the errors in discretization formulas, one usually hopes to obtain a mean value type of error. This occurs if the associated Peano kernel is a function which does not change sign. In this paper an expansion is developed which will express any error in mean value form, even when the associated Peano kernel is a function which changes sign.

**[1]**G. D. BIRKHOFF, "General mean value and remainder theorems with applications to mechanical differentiation and integration,"*Trans. Amer. Math. Soc.*, v. 7, 1906, pp. 107-136. MR**1500736****[2]**P. J. DAVIS & P. RABINOWITZ,*Methods of Numerical Integration*, Academic Press, New York, 1975. MR**0448814 (56:7119)****[3]**D. FERGUSON, "Sufficient conditions for Peano's kernel to be of one sign,"*SIAM J. Numer. Anal.*, v. 10, 1973, pp. 1047-1054. MR**0336969 (49:1742)****[4]**C. A. STEWART,*Advanced Calculus*, Methuen, London, 1940. MR**0001792 (1:299b)****[5]**A. H. STROUD, "Error estimates for Romberg quadrature,"*SIAM J. Numer. Anal.*, v. 2, 1965, pp. 480-488. MR**0201072 (34:957)****[6]**A. H. STROUD,*Numerical Quadrature and Solution of Ordinary Differential Equations*, Appl. Math. Series, Vol. 10, Springer-Verlag, New York, 1974. MR**0365989 (51:2241)****[7]**R. A. USMANI, "On improving error bounds in the integration of a boundary value problem,"*Bull. Calcutta Math. Soc.*, v. 70, 1978, pp. 33-43. MR**538192 (80e:65083)**

Retrieve articles in *Mathematics of Computation*
with MSC:
41A58,
65G99

Retrieve articles in all journals with MSC: 41A58, 65G99

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0572857-0

Article copyright:
© Copyright 1980
American Mathematical Society