Accession Number : AD0688960

Title :   INVESTIGATIONS ON THE EULER-MACLAURIN SUMMATION FORMULA AND ON NUMERICAL SOLUTION OF POLYNOMIAL EQUATIONS.

Descriptive Note : Final technical rept. 1 Jun 67-31 Mar 69,

Corporate Author : BASEL UNIV (SWITZERLAND) MATHEMATICS INST

Personal Author(s) : Ostrowski,Alexander M.

Report Date : APR 1969

Pagination or Media Count : 11

Abstract : A new form for the remainder of the Euler-Maclaurin summation formula is presented, while on the other hand the classical results are generalized in different directions. In particular the results of Jacobi and Malmsten are simplified and improved, introducing the convexity condition. The inequality of G. Gruss, given by him for functions of one variable is generalized to most general spaces, introducing the general linear means of functionals in such spaces. On the other hand new bounds for Gruss' expression are derived partly in connection with Tchebicheff's inequality. These bounds depend partly on maximum modulus of the derivative and partly on the integral quadratic mean of the derivative. (Author)

Descriptors :   (*SERIES(MATHEMATICS), CONVERGENCE), (*INTEGRALS, INEQUALITIES), (*POLYNOMIALS, NUMERICAL ANALYSIS), APPROXIMATION(MATHEMATICS), SEQUENCES(MATHEMATICS), SWITZERLAND

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE