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fixed-point methods


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1: 3.8 Nonlinear Equations
For fixed-point methods for computing zeros of special functions, see Segura (2002), Gil and Segura (2003), and Gil et al. (2007a, Chapter 7). …
§3.8(vii) Systems of Nonlinear Equations
For fixed-point iterations and Newton’s method for solving systems of nonlinear equations, see Gautschi (1997a, Chapter 4, §9) and Ortega and Rheinboldt (1970).
§3.8(viii) Fixed-Point Iterations: Fractals
2: Bibliography S
  • J. Segura (2002) The zeros of special functions from a fixed point method. SIAM J. Numer. Anal. 40 (1), pp. 114–133.
  • 3: Bibliography G
  • B. Gambier (1910) Sur les équations différentielles du second ordre et du premier degré dont l’intégrale générale est a points critiques fixes. Acta Math. 33 (1), pp. 1–55.
  • J. S. Geronimo, O. Bruno, and W. Van Assche (2004) WKB and turning point theory for second-order difference equations. In Spectral Methods for Operators of Mathematical Physics, Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
  • M. L. Glasser (1979) A method for evaluating certain Bessel integrals. Z. Angew. Math. Phys. 30 (4), pp. 722–723.
  • V. V. Golubev (1960) Lectures on Integration of the Equations of Motion of a Rigid Body About a Fixed Point. Translated from the Russian by J. Shorr-Kon, Office of Technical Services, U. S. Department of Commerce, Washington, D.C..
  • B. Guo (1998) Spectral Methods and Their Applications. World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.