Bibliography for Picard Iteration

unabridged

 

  1. Approximating fixed points of weak phi-contractions using the Picard iteration.  
    Berinde, Vasile
    Fixed Point Theory  4  (2003),  no. 2, 131--142, MathSciNet.  
  2. Gevrey and analytic convergence of Picard's successive approximations
    Shin, C. E.; Chung, S.-Y.; Kim, D.
    Integral Transforms and Special Functions, 2003, vol. 14, no. 1, pp. 19-30, Ingenta.  
  3. Iterates of some bivariate approximation process via weakly Picard operators
    Agratini, O.; Rus, I. A.
    Nonlinear Analysis Forum, 2003, vol. 8, no. 2, pp. 159-168, Ingenta.
  4. Picard Iteration for Nonsmooth Equations
    Sheng, Song-bai; Xu, Hui-fu
    Journal of Computational Mathematics, November, 2001, vol. 19, no. 6, pp. 583-590, MathSciNet.  
  5. A numerical radiative transfer model for a spherical planetary atmosphere: Combined differential-integral approach involving the Picard iterative approximation
    Rozanov, A.; Rozanov, V.; Burrows, J.P.
    Journal of Quantitative Spectroscopy and Radiative Transfer, v 69, n 4, May 15, 2001, p 491-512, Compendex.   
  6. Picard iterations for solution of nonlinear equations in certain Banach spaces.
    Moore, Chika
    J. Math. Anal. Appl. 245 (2000), no. 2, 317--325, MathSciNet.  
  7. C11 convergence of Picard's successive approximations  
    Izzo, Alexander J.
    Proceedings of the american mathematical society, 1999, vol. 127, no. 7, pp. 2059, Ingenta.  
  8. On a Theorem of Picard  
    F. Gesztesy; W. Sticka  
    Proceedings of the American Mathematical Society, Vol. 126, No. 4. (Apr., 1998), pp. 1089-1099, Jstor.  
  9. An Adaptive Newton--Picard Algorithm with Subspace Iteration for Computing Periodic Solutions  
    K. Lust, D. Roose
    SIAM Journal on Scientific Computing, Volume 19, Number 4, (1998), pp. 1188-1209.  
  10. Polynomial acceleration of the Picard-Lindelof iteration.
    Hyvonen, S.
    IMA journal of numerical analysis, 1998, vol. 18, no. 4, pp. 519, Ingenta.  
  11. Solution of the nonlinear transport equation using modified Picard iteration
    Huang, Kangle; Mohanty, Binayak P.; Leij, Feike J.; van Genuchten, M.Th.
    Advances in Water Resources, v 21, n 3, Mar 31, 1998, p 237-249, Compendex.  
  12. Convergence of the Arnoldi process when applied to the Picard-Lindelof iteration operator.
    Hyvonen, Saara  
    Journal of computational and applied mathematics, 1997, vol. 87, no. 2, pp. 303-320, Ingenta.  
  13. Exponential convergence of Picard iteration for integrating linear and nonlinear modally coupled equations of motion
    Fromme, Joseph A.; Golberg, Michael A.
    Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, v 1, 1997, p 838-848, Compendex.  
  14. Picard Iteration Method, Chebyshev Polynomial Approximation, and Global Numerical Integration of Dynamical Motions.
    Fukushima, Toshio
    The Astronomical journal, 1997, vol. 113, no. 5, pp. 1909, Ingenta.  
  15. The Picard iterative approximation to the solution of the integral equation of radiative transfer - Part II. Three-dimensional geometry.
    Kuo, Kwo-Sen; Weger, R.C.; Welch, R.M.; Cox, S.K.
    Journal of Quantitative Spectroscopy and Radiative Transfer, v 55, n 2, February, 1996, p 195-213, Ingenta.  
  16. Implementing the Picard iteration.
    Parker, G. Edgar; Sochacki, James S.
    Neural Parallel Sci. Comput. 4 (1996), no. 1, 97--112, MathSciNet.  
  17. A New convergence criterion for the modified Picard iteration method to solve the variably saturated flow equation
    Huang, K.; Mohanty, B.P.; van Genuchten, M. Th.
    Journal of Hydrology, v 178, n 1-4, Apr 15, 1996, p 69-91, Compendex.  
  18. Newton-Picard Methods with Subspace Iteration for Computing Periodic Solutions of Partial Differential Equations.
    Lust, K.; Rose, D.
    Zeitschrift fuer Angewandte Mathematik und Mechanik, ZAMM, Applied Mathematics and Mechanics, v 76, n Suppl 2, 1996, p 605, Ingenta.  
  19. The Picard Iterative approximation to the solution of the integral equation of radiative transfer - Part I. The plane-parallel case.
    Kuo, Kwo-Sen; Weger, Ronald C.; Welch, Ronald M.
    Journal of Quantitative Spectroscopy and Radiative Transfer, v 53, n 4, Apr, 1995, p 425, Ingenta.  
  20. Prediction of sound pressure fields by Picard-iterative BEM based on holographic interferometry
    Klingele, H.; Steinbichler, H.
    ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, v 4, Image and Multi-Dimensional Signal Processing, 1995, p 2727-2730, Compendex.  
  21. Convergence of Picard and modified Picard iterations for neutral functional-differential equations.
    Jackiewicz, Zdzislaw; Kwapisz, Marian
    Proceedings of the First International Conference on Difference Equations (San Antonio, TX, 1994), 263--272, Gordon and Breach, Luxembourg, 1995, MathSciNet.  
  22. A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems.
    Paniconi, Claudio; Putti, Mario
    Water resources research, 1994, vol. 30, no. 12, pp. 3357, Ingenta.  
  23. Parallel-in-time method based on shifted-picard iterations for power system transient stability analysis
    Brucoli, M.; De Roma, A.; La Scala, M.; Trovato, M.
    European Transactions on Electrical Power Engineering/ETEP, v 4, n 6, Nov-Dec, 1994, p 525-532, Compendex.  
  24. Picard iteration convergence analysis in a Galerkin finite element approximation of the one-dimensional shallow water equations.
    Cathers, B.; O'Connor, B. A.
    Numerical Methods for Partial Differential Equations, v 9, n 1, Jan, 1993, p 77-92, MathSciNet.  
  25. Efficiency of the application of Chebyshev polynomials in Picard's successive approximations for solving ordinary differential equations. (Russian)
    Bespalova, S. A.
    Latv. Mat. Ezhegodnik No. 34 (1993), 59--67, 275, MathSciNet.  
  26. The extension of Picard's successive approximation for constructing two-side bounds for the solutions of differential equations.
    Özics, Turgut
    Journal of computational and applied mathematics, 1992, vol. 39, no. 1, 7--14, MathSciNet.  
  27. Evaluation of the picard and newton iteration schemes for three-dimensional unsaturated flow
    Putti, M.; Paniconi, C.
    Finite Elements in Water Resources, Proceedings of the International Conference, v 1, 1992, p 529-536, Compendex.  
  28. Chebyshev acceleration of Picard-Lindelof iteration.
    Lubich, Ch.
    BIT, 1992, no. 3, pp. 535, Ingenta.  
  29. An analysis of the convergence of Picard iterations for implicit approximations of Richard's equation.
    Aldama, A. A.; Paniconi, C.
    Computational methods in water resources, IX, Vol. 1 (Denver, CO, 1992), 521--528, Comput. Mech., Southampton, 1992, MathSciNet.  
  30. Quasinilpotency of the Operators in Picard-Lindelof Iteration.
    Miekkala, U.; Nevanlinna, O.
    Numerical Functional Analysis and Optimization, v 13, n 1-2, Feb-Apr, 1992, p 203, Ingenta.  
  31. Power bounded prolongations and Picard-Lindelof iteration.
    Nevanlinna, O.
    Numerische mathematik, 1990, vol. 58, no. 5, pp. 479, Ingenta.  
  32. Linear Acceleration of Picard-Lindelof Iteration.
    Nevanlinna, O.
    Numerische mathematik, 1990, vol. 57, no. 2, pp. 147, Ingenta.  
  33. Quasi-Picard iteration convergence theorems for sequences of contractive mappings in probabilistic metric spaces. (Chinese)
    Cai, Chang Lin
    J. Chengdu Univ. Sci. Tech. 1990, no. 6, 93--98, MathSciNet.  
  34. Symbolic Computational Algebra Applied to Picard Iteration
    Mathews, John
    Mathematics and Computer Education Journal, 1989, Vol. 23, No. 2, pp. 117, Ingenta.  
  35. Remarks on Picard-Lindelof iteration: Part II.
    Nevanlinna, O.
    BIT, 1989, no. 3, pp. 535, Ingenta.  
  36. Waveform Iteration and the Shifted Picard Splitting.
    Skeel, Robert D.
    Siam journal on scientific and statistical compu, 1989, vol. 10, no. 4, pp. 756, Ingenta.  
  37. A note on the convergence of Picard iteration for solving Volterra equations of the second kind. (Chinese)
    Zhang, Guan Quan
    Math. Numer. Sinica 11 (1989), no. 1, 110--112; translation in Chinese J. Numer. Math. Appl. 11 (1989), no. 2, 109--111, MathSciNet.  
  38. Comparison of Picard and Newton iterative methods for unconfined groundwater flows
    Mohan Kumar, M.S.; Sridharan, K.; Lakshmana Rao, N.S.
    Journal of the Institution of Engineers (India), Part CI: Civil Engineering Division, v 68 pt 6, May, 1988, p 266-271, Compendex.  
  39. Convergence theorems for the generalized quasi-Picard iteration of a contraction mapping in probabilistic metric spaces. (Chinese)
    Kang, Shi Kun; Xiong, Tian Xiang
    J. Chengdu Univ. Sci. Tech. 1987, no. 2, 131--141, MathSciNet.  
  40. Convergence rate estimation of Picard iteration sequences for a class of contraction mappings in probabilistic metric spaces. (Chinese)
    Xiong, Tian Xiang; Kang, Shi Kun
    J. Chengdu Univ. Sci. Tech. 1987, no. 1, 75--78, 84, MathSciNet.  
  41. Application of picard-chebyshev iteration and an extended procedure to an elastica problem
    Chakrabarti, S.; Rao, C.V. Joga
    Congress of the Indian Society of Theoretical and Applied Mechanics, 1985, p 207, Compendex.  
  42. Picard Iterations Of Boundary-Layer Equations.
    Ardema, M. D.; Yang, L.
    AIAA Paper, 1985, p 669-678, Compendex.  
  43. Some experiments with Picard's iteration for second-order nonlinear boundary value problems.
    Meek, D. S.; Usmani, R. A.
    Proceedings of the fourteenth Manitoba conference on numerical mathematics and computing (Winnipeg, Man., 1984). Congr. Numer. 46 (1985), 201--210, MathSciNet.  
  44. Role Of Semiconductor Device Diameter And Energy-Band Bending In Convergence Of Picard Iteration For Gummel's Map.
    Jerome, Joseph W.  
    IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, v CAD-4, n 4, Oct, 1984, p 489-495, Compendex.  
  45. Computing solution branches by use of a condensed Newton-supported Picard iteration scheme.
    Jarausch, H.; Mackens, W.
    Z. Angew. Math. Mech. 64 (1984), no. 5, 282--284, MathSciNet.  
  46. A mixed Newton-Picard-iteration for the solution of nonlinear two-point boundary value problems.
    Mackens, W.
    Proceedings of the Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik, Würzburg 1981, Part II (Würzburg, 1981). Z. Angew. Math. Mech. 62 (1982), no. 5, T334--T336, MathSciNet.  
  47. A comparison of the iterative method and Picard's successive approximations for deterministic and stochastic differential equations.
    Adomian, G.; Malakian, K.
    Appl. Math. Comput. 8 (1981), no. 3, 187--204, MathSciNet.  
  48. Convergence theorems of quasi-Picard iteration of a contraction mapping on probabilistic metric spaces. (Chinese)
    You, Zhao Yong
    J. Math. Res. Exposition 1981, First Issue, 25--28, MathSciNet.  
  49. A Relaxed Picard Iteration Process for Set-Valued Operators of the Monotone Type  
    J. C. Dunn  
    Proceedings of the American Mathematical Society, Vol. 73, No. 3. (Mar., 1979), pp. 319-327, Jstor.  
  50. Volterra Series And Picard Iteration For Nonlinear Circuits And Systems.
    Leon, Benjamin J.; Schaefer, Daniel J.
    Special issue on the mathematical foundations of system theory. IEEE Trans. Circuits and Systems 25 (1978), no. 9, 789--793, MathSciNet.  
  51. Solutions Of The Diffusion Equation By Picard's Iteration Procedure.
    Moalem-Maron, D.; Meinhardt, Y. Roberto
    Letters in Heat and Mass Transfer, v 5, n 5, Sep-Oct, 1978, p 269-277, Compendex.  
  52. Self-Regulating Picard-Type Iteration For Computing The Periodic Response Of A Nearly Linear Circuit To A Periodic Input.
    Neill, T. B. M.; Stefani, Jane
    Electronics Letters, v 11, n 17, Aug 21, 1975, p 413-415, Compendex.  
  53. Picard's Theorem (in Classroom Notes)  
    James Fabrey  
    The American Mathematical Monthly, Vol. 79, No. 9. (Nov., 1972), pp. 1020-1023, Jstor.  
  54. On the region of convergence of Picard's iteration.
    van de Craats, J.
    Z. Angew. Math. Mech. 52 (1972), no. 9, 487--491, MathSciNet.  
  55. An extended Picard iteration scheme.
    Ponzo, Peter J.
    Utilitas Math. 2 (1972), 133--139, MathSciNet.  
  56. On Iteration Procedures for Equations of the First Kind, Ax = y, and Picard's Criterion for the Existence of a Solution  
    J. B. Diaz; F. T. Metcalf  
    Mathematics of Computation, Vol. 24, No. 112. (Oct., 1970), pp. 923-935, Jstor.  
  57. Convergence of Picard's Method for |lambda| > |lambda1| (in Mathematical Notes)  
    J. W. Burgmeier; M. R. Scott  
    The American Mathematical Monthly, Vol. 77, No. 8. (Oct., 1970), pp. 865-867, Jstor.  
  58. On the interval of convergence of Picard's iteration.
    Bailey, P. B.
    Z. Angew. Math. Mech. 48 1968 127--128, MathSciNet.  
  59. On the Cauchy-Picard Method  
    Arthur Wouk  
    The American Mathematical Monthly, Vol. 70, No. 2. (Feb., 1963), pp. 158-162, Jstor.  
  60. Note on the Picard Method of Successive Approximations  
    Dunham Jackson  
    The Annals of Mathematics, 2nd Ser., Vol. 23, No. 1. (Sep., 1921), pp. 75-77, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004