Bibliography for the Regula Falsi Method

unabridged

  1. Die verallgemeinerte Regula falsi und das Matrizen-Eigenwertproblem
    Budich, H.; Falk, S.
    Zeitschrift fur Angewandte Mathematik und Mechanik, 2001, vol. 81, no. SUPP/4, pp. S1007-1008, Ingenta.  
  2. Contraction, Robustness, and Numerical Path-Following Using Secant Maps
    Jean-Claude Yakoubsohn
    Journal of Complexity, Vol. 16, No. 1, Mar 2000, pp. 286-310, Ideal.  
  3. Finding zeros of analytic functions: alpha theory for secant type methods.
    Yakoubsohn, Jean-Claude
    J. Complexity 15 (1999), no. 2, 239--281, MathSciNet.  
  4. An object-oriented approach to numerical methods: the Regula Falsi method for solving equations with tight tolerances for environmental applications.
    Author: Phillips, J. B.; Price, G.; Fry, S.
    Journal of Hazardous Materials v. 63 no2-3 (Dec. 1 '98) p. 145-62, FirstSearch.  
  5. An acceleration procedure of regula falsi method.  
    Hernández, M. A.; Salanova, M. A.
    Tamkang journal of mathematics, 1997, vol. 28, no. 1, 67--77, MathSciNet.  
  6. Global convergence of the regula falsi method for the equation. (Japanese)
    Yamagishi, Yoshikazu
    Theory and application of numerical calculation in science and technology, II (Japanese) (Kyoto,1996),
    Surikaisekikenkyusho Kokyuroku No. 990 (1997), 244--249, MathSciNet.  
  7. Modification of the Regula Falsi method to accelerate system convergence in the prediction of trace quantities of atmospheric pollutants.
    Phillips, J.B.; Menawat, A.S.; Carden, S.R.
    Journal of hazardous materials, 1995, vol. 44, no. 1, pp. 25, Ingenta.  
  8. On iteration methods without derivatives for the simultaneous determination of polynomial zeros. J.
    Carstensen, Carsten; Petkovic, Miodrag S.
    Comput. Appl. Math. 45 (1993), no. 3, 251--266, MathSciNet.  
  9. On the algebraic complexity of rational iteration procedures.
    Baur, Walter
    Theoret. Comput. Sci. 88 (1991), no. 2, 313--324, MathSciNet.  
  10. Improved regula falsi method for solving the Schrödinger equation with a piecewise constant potential.
    Friedman, M.; Rabinovitch, A.
    J. Comput. Phys. 68 (1987), no. 1, 180--187, MathSciNet.  
  11. Computing area filling contours for surfaces defined by piecewise polynomials.
    Preusser, Albrecht
    Comput. Aided Geom. Design 3 (1986), no. 4, 267--279 (1987), MathSciNet.  
  12. Was ist das Falsche an der Regula Falsi? (German) [What is ``wrong'' with the regula falsi?]
    Maas, Christoph
    Mitt. Math. Ges. Hamburg 11 (1985), no. 3, 311--317, MathSciNet.  
  13. An example for the regula-falsi method with an asymptotic cycle.
    Dietze, S.
    Computing 33 (1984), no. 1, 75--81, MathSciNet.  
  14. Some remarks about the monotone inclusion for solutions of nonlinear equations by regula-falsi-like methods. With a loose Russian summary.
    Schneider, Norbert
    Apl. Mat. 28 (1983), no. 1, 21--31, MathSciNet.  
  15. Exit criteria for some iterative methods.
    Herceg, Dragoslav
    Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 12 (1982), 139--149, MathSciNet.  
  16. An application of the induction method of V. Pták to the study of regula falsi. With a loose Russian summary.
    Potra, Florian-Alexandru
    Apl. Mat. 26 (1981), no. 2, 111--120, MathSciNet.  
  17. Monotone Einschließung durch Verfahren vom Regula-falsi-Typ unter Verwendung eines verallgemeinerten Steigungsbegriffes. (German)
    Schneider, N.
    Computing 26 (1981), no. 1, 33--44, MathSciNet.  
  18. A generalization of regula falsi.
    Potra, Florian-A.; Pták, Vlastimil
    Numer. Math. 36 (1980/81), no. 3, 333--346, MathSciNet.  
  19. Nondiscrete induction and a double step secant method.
    Potra, F.-A.; Pták, Vlastimil
    Math. Scand. 46 (1980), no. 2, 236--250, MathSciNet.  
  20. On an iterative improvement of the approximate solution of some ordinary differential equations.
    Zadunaisky, P. E.; Lafferriere, G.
    Comput. Math. Appl. 6 (1980), no. 1, Special Issue, 147--154, MathSciNet.  
  21. Monotone Regula-falsi-ähnliche Verfahren bei nichtkonvexen Operatorgleichungen. (German)
    Alefeld, Götz
    Beiträge Numer. Math. 8 (1980), 15--30, MathSciNet.  
  22. The Pegasus methods for the solution of nonlinear equations. (Hungarian)
    Kalmár, János
    Alkalmaz. Mat. Lapok 5 (1979), no. 3-4, 277--288 (1980), MathSciNet.  
  23. Convergence of a class of iterative methods of regula falsi type. (Russian)
    Safiev, R. A.; Babaeva, A. È.
    Izv. Akad. Nauk Azerbadzhan. SSR Ser. Fiz.-Tekhn. Mat. Nauk 1979, no. 6, 52--58, MathSciNet.  
  24. The Rule of False applied to the quadratic equation, in three sixteenth century arithmetics.
    Smeur, A. J. E. M.
    Arch. Internat. Hist. Sci. 28 (1978), no. 102, 66--101, MathSciNet.  
  25. Untere Fehlerschranken für Regula-Falsi-Verfahren. (German)
    Schmidt, J. W.
    Period. Math. Hungar. 9 (1978), no. 3, 241--247, MathSciNet.  
  26. A secant method for multiple roots. Nordisk Tidskr.
    King, Richard F.
    Informationsbehandling (BIT) 17 (1977), no. 3, 321--328, MathSciNet.  
  27. A generalized secant method and the regula falsi method in the solution of nonlinear functional equations of potential type. (Russian)
    Simeonov, S. V.
    C. R. Acad. Bulgare Sci. 30 (1977), no. 7, 959--962, MathSciNet.  
  28. Methods without secant steps for finding a bracketed root.
    King, R. F.
    Computing 17 (1976), no. 1, 49--57, MathSciNet.  
  29. Simplicial methods for the solution of systems of nonlinear equations.
    Bittner, Leonhard
    Z. Angew. Math. Mech. 56 (1976), no. 2, 65--73, MathSciNet.  
  30. Regula-falsi-Verfahren mit konsistenter Steigung und Majorantenprinzip. (German)
    Schmidt, J. W.
    Period. Math. Hungar. 5 (1974), 187--193, MathSciNet.  
  31. An improved Pegasus method for root finding.
    King, Richard F.
    Nordisk Tidskr. Informationsbehandling(BIT) 13 (1973), 423--427, MathSciNet.  
  32. A new high order method of regula falsi type for computing a root of an equation.
    Anderson, Ned; Björck, Ake
    Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 253--264, MathSciNet.  
  33. Untersuchung einer nichtlinearen regula falsi.
    Dittmann, Gerd
    Wiss. Z. Hochsch. Verkehrswesen "Friedrich List" Dresden 20 (1973), no. 4, 733--739, MathSciNet.  
  34. Überlinear konvergente Mehrschrittverfahren vom Regula falsi- und Newton-Typ. (German)
    Schmidt, J. W.
    Z. Angew. Math. Mech. 53 (1973), no. 2, 103--114, MathSciNet.  
  35. The "Pegasus" method for computing the root of an equation.
    Dowell, M.; Jarratt, P.
    Nordisk Tidskr. Informationsbehandling (BIT) 12 (1972), 503--508, MathSciNet.  
  36. Konvergenzsätze für Regula-falsi-Verfahren. (German)
    Hofmann, Wolf
    Arch. Rational Mech. Anal. 44 (1971/72), 296--309, MathSciNet.  
  37. A modified Regula Falsi method for computing the root of an equation.
    Dowell, M.; Jarratt, P.
    Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 168--174, MathSciNet.  
  38. On the rapidity of convergence of sequences of errors in the methods of Newton and of regula falsi.
    Hyzy, Andrzej
    Zeszyty Nauk. Uniw. Jagiello. Prace Mat. No. 15 (1971), 67--69, MathSciNet.  
  39. Die Regula falsi in Banach-Räumen. (German)
    Hofmann, W.
    Computing (Arch. Elektron. Rechnen) 7 (1971), 106--112, MathSciNet.  
  40. Monotoniesätze für Regula-falsi- und Newton-Verfahren. (German)
    Hofmann, W.
    Computing (Arch. Elektron. Rechnen) 8 (1971), 143--156, MathSciNet.  
  41. The numerical treatment of a single nonlinear equation.
    Householder, A. S.
    International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York-Düsseldorf-London, 1970. viii+216 pp, MathSciNet.  
  42. Eingrenzung von Lösungen mit Hilfe der Regula falsi. (German)
    Schmidt, J. W.; Leonhardt, H.
    Computing (Arch. Elektron. Rechnen) 6 1970 318--329, MathSciNet.  
  43. 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.  
  44. Die Regula falsi für Systeme konvexer Gleichungen. (German)
    Rieger, G. J.
    Math. Nachr. 40 1969 145--164, MathSciNet.  
  45. Eine Verallgemeinerung der Regula Falsi auf Operatorgleichungen. (German)
    Homuth, H.-H.
    Z. Angew. Math. Mech. 47 1967 T51--T52, MathSciNet.  
  46. Interpolative Solution of Systems of Nonlinear Equations  
    Stephen M. Robinson  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 4. (Dec., 1966), pp. 650-658, Jstor.  
  47. La comparaison de la rapidité de convergence des approximations successives de la méthode de Newton avec la méthode de "regula falsi". (French)
    Gopolhk, S.
    Mathematica (Cluj) 8 (31) 1966 45--49, MathSciNet.  
  48. Generalization of Steffensen's method for operator equations.
    Chen, Kuo-Wang
    Comment. Math. Univ. Carolinae 5 1964 47--77, MathSciNet.  
  49. Eine Übertragung der Regula Falsi auf Gleichungen in Banachräumen. II. Nichtlineare Gleichungssysteme. (German)
    Schmidt, Jochen W.
    Z. Angew. Math. Mech. 43 1963 97--110, MathSciNet.  
  50. Regula Falsi and the Fibonacci Numbers (in Classroom Notes)  
    Dmitri Thoro  
    American Mathematical Monthly, Vol. 70, No. 8. (Oct., 1963), p. 869, Jstor.  
  51. Eine Übertragung der Regula Falsi auf Gleichungen in Banachräumen. I. (German)
    Schmidt, Jochen W.
    Z. Angew. Math. Mech. 43 1963 1--8, MathSciNet.  
  52. Eine Verallgemeinerung des Sekantenverfahrens (regula falsi) zur näherungsweisen Berechnung der Nullstellen eines nichtlinearen Gleichungssystems. (German)
    Bittner, Leonhard
    Wiss. Z. Techn. Hochsch. Dresden 9 1959/1960 325--329, MathSciNet.  
  53. Solution of certain large sets of equations on Pegasus using matrix methods.
    Wilson, L. B.
    Comput. J. 2 1959 130--133, MathSciNet.  
  54. The method of regula falsi for solving integral equations. (Spanish)
    Velasco de Pando, Manuel
    Rev. Acad. Ci. Madrid 51 1957. 139--147, MathSciNet.  
  55. The method of regula falsi for solving integral equations. (Spanish)  
    Velasco de Pando, Manuel
    Dyna 1956 1956 no. 4, 3--4: no. 9, 2--3, MathSciNet.  
  56. Principe de Rayleigh et regula falsi de Newton. (French) Acad. Roy.
    van den Dungen, F. H.
    Belgique. Bull. Cl. Sci. (5) 38, (1952). 695--704, MathSciNet.  
  57. Über eine Verallgemeinerung des Verfahrens der Kombination von Newton'scher Methode und Regula falsi zur Auflösung einer Gleichung f(x)=0. (German)
    Pflanz, Erwin
    Z. Angew. Math. Mech. 28, (1948). 114--122, MathSciNet.  
  58. Über eine praktische Anwendung der Regula Falsi. (German)
    Leemann, W.
    Schweiz. Z. Vermessgswes. Kulturtech. 41, (1943). 276--278, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003