# iterative methods

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## 1—10 of 12 matching pages

##### 2: 29.20 Methods of Computation
A second approach is to solve the continued-fraction equations typified by (29.3.10) by Newton’s rule or other iterative methods; see §3.8. …
##### 4: Bibliography T
• J. F. Traub (1964) Iterative Methods for the Solution of Equations. Prentice-Hall Series in Automatic Computation, Prentice-Hall Inc., Englewood Cliffs, N.J..
• ##### 5: Bibliography S
• B. I. Schneider, X. Guan, and K. Bartschat (2016) Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation. Adv. Quantum Chem. 72, pp. 95–127.
• ##### 6: 3.11 Approximation Techniques
to $f(x)$, then the coefficients $a_{k}$ can be computed iteratively. … The iterative process converges locally and quadratically (§3.8(i)). A method for obtaining a sufficiently accurate first approximation is described in the next subsection. … For details and examples of these methods, see Clenshaw (1957, 1962) and Miller (1966). … The method of the fast Fourier transform (FFT) exploits the structure of the matrix $\boldsymbol{{\Omega}}$ with elements $\omega_{n}^{jk}$, $j,k=0,1,\dots,n-1$. …
##### 7: 19.36 Methods of Computation
###### §19.36(i) Duplication Method
When the differences are moderately small, the iteration is stopped, the elementary symmetric functions of certain differences are calculated, and a polynomial consisting of a fixed number of terms of the sum in (19.19.7) is evaluated. …
###### §19.36(iv) Other Methods
Numerical quadrature is slower than most methods for the standard integrals but can be useful for elliptic integrals that have complicated representations in terms of standard integrals. …
##### 8: Bibliography G
• B. Gabutti and G. Allasia (2008) Evaluation of $q$-gamma function and $q$-analogues by iterative algorithms. Numer. Algorithms 49 (1-4), pp. 159–168.
• B. Gabutti (1979) On high precision methods for computing integrals involving Bessel functions. Math. Comp. 33 (147), pp. 1049–1057.
• B. Gabutti (1980) On the generalization of a method for computing Bessel function integrals. J. Comput. Appl. Math. 6 (2), pp. 167–168.
• M. L. Glasser (1979) A method for evaluating certain Bessel integrals. Z. Angew. Math. Phys. 30 (4), pp. 722–723.
• B. Guo (1998) Spectral Methods and Their Applications. World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.
• ##### 9: 22.20 Methods of Computation
###### §22.20 Methods of Computation
Four iterations of (22.20.1) lead to $c_{4}=\Sci{6.5}{-12}$. … If $k=k^{\prime}=1/\sqrt{2}$, then three iterations of (22.20.1) give $M=0.84721\;30848$, and from (22.20.6) $K=\pi/(2M)=1.85407\;46773$ — in agreement with the value of $\left(\Gamma\left(\tfrac{1}{4}\right)\right)^{2}/\left(4\sqrt{\pi}\right)$; compare (23.17.3) and (23.22.2). … If $k^{\prime}=1-i$, then four iterations of (22.20.1) give $K=1.23969\;74481+i0.56499\;30988$. … For additional information on methods of computation for the Jacobi and related functions, see the introductory sections in the following books: Lawden (1989), Curtis (1964b), Milne-Thomson (1950), and Spenceley and Spenceley (1947). …
##### 10: Bibliography O
• A. M. Odlyzko (1995) Asymptotic Enumeration Methods. In Handbook of Combinatorics, Vol. 2, L. Lovász, R. L. Graham, and M. Grötschel (Eds.), pp. 1063–1229.
• T. Oliveira e Silva (2006) Computing $\pi(x)$: The combinatorial method. Revista do DETUA 4 (6), pp. 759–768.
• J. Oliver (1977) An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.
• F. W. J. Olver (1950) A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations. Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.
• J. M. Ortega and W. C. Rheinboldt (1970) Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York.