Bibliography for Romberg Integration

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  1. Romberg quadrature using the Bulirsch sequence
    Fischer, J.-W.
    Numerische Mathematik, 2002, vol. 90, no. 3, pp. 509-520, MathSciNet.   
  2. On complexity of Romberg and adaptive-recursive numerical integration methods.
    Coman, Gheorghe; Trîmbitas, Radu T.
    Mathematica 40(63) (1998), no. 1, 63--70, MathSciNet.   
  3. A Short Proof for Romberg Integration (in Notes)  
    T. von Petersdorff  
    American Mathematical Monthly, Vol. 100, No. 8. (Oct., 1993), pp. 783-785, Jstor.  
  4. Romberg integration and classical analysis.
    Håvie, Tore
    Romberg Seminar on Quadrature/Interpolation/Extrapolation and Rational Approximations (Padé-continued Fractions) (Trondheim, 1988). Skr. K. Nor. Vidensk. Selsk. 1989, no. 2, 60--72, MathSciNet.   
  5. Romberg Integration: A QuickBASIC Subroutine.
    Noggle, Joseph H.
    Access, 1988, vol. 7, no. 5, pp. 20 , Ingenta.  
  6. Romberg Integration by Taylor Series (in Notes)  
    Edward R. Rozema  
    American Mathematical Monthly, Vol. 94, No. 3. (Mar., 1987), pp. 284-288, Jstor.  
  7. Remarks on some modified Romberg algorithms for numerical integration.
    Håvie, Tore  
    Numerical mathematics and applications (Oslo, 1985), 57--63, IMACS Trans. Sci. Comput.---85, I, North-Holland, Amsterdam, 1986, MathSciNet.   
  8. On forming the Romberg table.
    Shanks, J. A.
    J. Comput. Appl. Math. 11 (1984), no. 3, 343--351, MathSciNet.   
  9. Richardson Extrapolation and Romberg Integration  
    Jacques Dutka  
    Historia Mathematica, Vol.  11, No. 1, (February 1984), pp 3-21, MathSciNet.   
  10. Analysis of certain possibility for parallel treatment of the Romberg quadrature algorithm.
    Chiruta, Constantin
    An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 28 (1982), no. 2, suppl., 101--104, MathSciNet.   
  11. Cautious Romberg extrapolation.
    Cohen, A. M.
    Internat. J. Comput. Math. 8 (1980), no. 2, 137--147, MathSciNet.   
  12. Romberg integration as a problem in interpolation theory.  
    Håvie, Tore
    Nordisk Tidskr. Informationsbehandling (BIT) 17 (1977), no. 4, 418--429, MathSciNet.  
  13. Propagation Of Initial Rounding Error In Romberg-Like Quadrature.  
    Laurie, D. P.; (Natl Res Inst for Math Sci, Pretoria, S Afr);
    Nordisk Tidskr. Informationsbehandling BIT (Copenhagen), v 15, n 3, 1975, p 277-282, Compendex.  
  14. On The Exit Criteria For The Romberg Integration Scheme Em Dash A Pragmatic Approach.  
    Robinson, Ian; (Univ of Melbourne, Victoria, Aust);
    Australian Computer Journal, v 7, n 3, Nov, 1975, p 113-115, MathSciNet.  
  15. Monotonicity in Romberg Quadrature  
    Torsten Strom  
    Mathematics of Computation, Vol. 26, No. 118. (Apr., 1972), pp. 461-465, Jstor.  
  16. Error derivation in Romberg integration.  
    Håvie, Tore
    Nordisk Tidskr. Informationsbehandling (BIT) 12 (1972), 516--527, MathSciNet.  
  17. Romberg tables for singular integrands.
    Shanks, J. A.
    Comput. J. 15 (1972), 360--361, MathSciNet.   
  18. An algorithm for Gauss-Romberg integration.  
    Lyness, J. N.  
    Nordisk Tidskr. Informationsbehandling (BIT) 12 (1972), 194--203, MathSciNet.  
  19. Generalized Romberg methods for integrals of derivatives.  
    Lyness, J. N.; Moler, C. B.  
    Numer. Math. 14 1969/1970 1--13, MathSciNet.   
  20. Neville's and Romberg's Processes: A Fresh Appraisal with Extensions  
    J. C. P. Miller  
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 263, No. 1144. (Dec. 24, 1968), pp. 525-562, Jstor.  
  21. On a modification of Romberg quadrature.
    Manohar, R.; Turnbull, C.
    Canad. Math. Bull. 11 1968 217--224, MathSciNet.   
  22. Romberg's method for certain integrals involving a singularity.
    Hunter, D. B.
    Nordisk Tidskr. Informations-Behandling (BIT) 7 1967 200--205, MathSciNet.   
  23. Romberg integration for a class of singular integrands.
    Fox, L.
    Comput. J. 10 1967 87--93, MathSciNet.   
  24. An extension of Romberg integration procedures to N-variables.
    Anders, Edward B.
    J. Assoc. Comput. Mach. 13 1966 505--510, MathSciNet.   
  25. On a modification of Romberg's algorithm.
    Håvie, Tore  
    Nordisk Tidskr. Informations-Behandling 6 1966 24--30, MathSciNet.   
  26. On the Method of Romberg Quadrature  
    A. Meir, A. Sharma  
    Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis, Vol. 2, No. 2. (1965), pp. 250-258, Jstor.  
  27. Error Estimates for Romberg Quadrature  
    A. H. Stroud  
    Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis, Vol. 2, No. 3. (1965), pp. 480-488 , Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

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