Bibliography for

Aitken's [Graphics:../Images/AitkenSteffensenBib_gr_5.gif]Method and Steffensen's Acceleration

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  1. Aitken-Based Acceleration Methods for Assessing Convergence of Multilayer Neural Networks
    Pilla, R. S.; Kamarthi, S. V.; Lindsay, B. G.
    IEEE Transactions on Neural Networks, 2001, vol. 12, no. 5, pp. 998-1012 , Ingenta.  
  2. Steffensen-Aitken methods and implicit functions.
    Argyros, Ioannis K.
    Panamer. Math. J. 11 (2001), no. 1, 91--96, MathSciNet.  
  3. On the convergence of Steffensen-Aitken-like methods using divided differences obtained recursively.
    Argyros, Ioannis K.; Catinas, Emil; Pavaloiu, Ion
    Adv. Nonlinear Var. Inequal. 3 (2000), no. 1, 7--13, MathSciNet.  
  4. Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences.
    Pavaloiu, I.
    Calcolo 32 (1995), no. 1-2, 69--82 (1996), MathSciNet.   
  5. The condition of Steffensen's acceleration in several variables.
    Nievergelt, Yves
    J. Comput. Appl. Math. 58 (1995), no. 3, 291--305, MathSciNet.   
  6. Aitken's and Steffensen's accelerations in several variables.   
    Nievergelt, Yves   
    Numer. Math. 59 (1991), no. 3, 295--310, MathSciNet.  
  7. A Convergence Acceleration Method for Some Logarithmically Convergent Sequences  
    Naoki Osada  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 1. (Feb., 1990), pp. 178-189, Jstor.  
  8. Numerical Methods of Mathematical Physics: Iterative Regularization of Steffensen's Method.
    Vasil'ev, F. P.
    Computational mathematics and modeling, 1990, vol. 1, no. 1, pp. 1, Ingenta.  
  9. Aitken Sequences and Fibonacci Numbers  
    G. M. Phillips  
    American Mathematical Monthly, Vol. 91, No. 6. (Jun. - Jul., 1984), pp. 354-357, Jstor.  
  10. Convergence property of Aitken's [Graphics:../Images/AitkenSteffensenBib_gr_6.gif]-process and the applicable acceleration process.   
    Iguchi, Ken   
    J. Inform. Process. 7 (1984), no. 1, 22--30, MathSciNet.  
  11. Aitken acceleration of some alternating series.
    Bell, G. E.; Phillips, G. M.
    BIT 24 (1984), no. 1, 70--77, MathSciNet.  
  12. Convergence Acceleration by Extraction of Linear Subsequences  
    C. Brezinski, J. P. Delahaye, B. Germain-Bonne  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 6. (Dec., 1983), pp. 1099-1105, Jstor.  
  13. On the Acceleration of an Interval-Arithmetic Iteration Method  
    Herbert Cornelius  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 5. (Oct., 1983), pp. 1010-1022, Jstor.  
  14. Anderson-Bjorck for Linear Sequences  
    Richard F. King  
    Mathematics of Computation, Vol. 41, No. 164. (Oct., 1983), pp. 591-596, Jstor.  
  15. Some New Convergence Acceleration Methods  
    Claude Brezinski  
    Mathematics of Computation, Vol. 39, No. 159. (Jul., 1982), pp. 133-145, Jstor.  
  16. Convergence Acceleration for Newton's Method at Singular Points  
    D. W. Decker, C. T. Kelley  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 1. (Feb., 1982), pp. 219-229, Jstor.  
  17. Extrapolation of asymptotic expansions by a modified Aitken [Graphics:../Images/AitkenSteffensenBib_gr_7.gif]-formula.   
    Bjørstad, Petter; Dahlquist, Germund; Grosse, Eric
    BIT 21 (1981), no. 1, 56--65, MathSciNet.  
  18. A note on the generalisation of Aitken's [Graphics:../Images/AitkenSteffensenBib_gr_8.gif] transformation.   
    Jamieson, M. J.; O'Beirne, T. H.   
    J. Phys. B 11 (1978), no. 2, L31--L35, MathSciNet.  
  19. On Aitken' s [Graphics:../Images/AitkenSteffensenBib_gr_9.gif] Method (in Mathematical Notes)  
    Simeon Reich  
    American Mathematical Monthly, Vol. 77, No. 3. (Mar., 1970), pp. 283-284., Jstor.  
  20. A Family of Functional Iterations and the Solution of Maximum Likelihood Estimating Equations  
    Leon L. Wegge  
    Econometrica, Vol. 37, No. 1. (Jan., 1969), pp. 122-130, Jstor.  
  21. On Steffensen's Method  
    L. W. Johnson, D. R. Scholz  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 2. (Jun., 1968), pp. 296-302, Jstor.  
  22. Aitken acceleration.
    Overholt, K. J. Extended
    Nordisk Tidskr. Informations-Behandling 5 1965 122--132, MathSciNet.  
  23. Solution of equations and systems of equations.
    Ostrowski, A. M.
    Pure and Applied Mathematics, Vol. IX. Academic Press, New York-London 1960 ix+202 pp, MathSciNet.  
  24. Some Applications of Aitken's Method of Interpolation (in Classroom Notes)  
    L. A. Aroian  
    American Mathematical Monthly, Vol. 55, No. 9. (Nov., 1948), pp. 569-572, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003