Composite quadratures for functions of dominated variation

References

• Bertrandias , J.P. 1960 . Calcul d'une integrate au moyen de la suite Xn = An. Evaluation de 1'erreur . Pub. Inst. Statist. Univ. Paris , 9 : 335 – 357 .
   Google Scholar
• Davis , P.J. and Rabinowitz , P. 1965 . Ignoring the singularity in approximate integration . J. Soc, Indust. Appl. Math. Ser. B Numer. Anal. , 2 : 367 – 383 .
   Google Scholar
• El-Tom , M.A. 1971 . On ignoring the singularity in approximate integration . SIAM,J.Numer. Anal. , 8 : 412 – 424 .
   Google Scholar
• Feldstein , M.A. and Miller , R.K. 1971 . Error bounds for compound quadratures of weakly singular integrals . Math. Comp. , 25 : 505 – 520 .
   Google Scholar
• Gautschi , W. 1967 . Numerical quadrature in the presence of a singularity . SI AM J.Numer. Anal. , 4 : 357 – 362 .
   Google Scholar
• Haber , S. and Shisha , O. 1974 . Improper integrals, simple integrals, and numerical quadrature . J.Approx. Theory. , 11 : 1 – 15 .
   Google Scholar
• Isaacson , E. and Keller , M.B. 1966 . Analysis of Numerical Methods , Wiley .
   Google Scholar
• Lubinsky , D.S. and Rabinowitz , P. 1984 . Rates of convergence of Gaussian quadratures for singular integrands . Math. Comp. , 43 : 219 – 242 .
   Web of Science ®Google Scholar
• Miller , R.K. 1971 . On ignoring the singularity in numerical quadrature . Math. Comp. , 25 : 521 – 532 .
   Google Scholar
• Osgood and Shisha . 1976 . The dominated integral . J.Approx. Theory , 17 : 150 – 165 .
   Google Scholar
• Osgood , C.F. and Shisha , O. 1977 . Numerical quadrature of improper integrals and the dominated integral . J. Approx. Theory4ei: , 20 : 139 – 152 .
   Web of Science ®Google Scholar
• Rabinowitz , P. 1967 . Gaussian integration in the presence of a singularity . SI AM J. Numer. Anal. , 4 : 191 – 201 .
   Google Scholar
• Tavernini , L. 1977 . Finite difference approximations for a class of semilinear Volterra evolution problems . SIAM J. Numer. Anal.4ei: , 14 : 931 – 949 .
   Web of Science ®Google Scholar
• Zaremba , S.K. 1966 . Good lattice points, discrepancy, and numerical integration . Annalidi Matematica , 73 : 293 – 317 .
   Google Scholar