complex arithmetic
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1: 3.1 Arithmetics and Error Measures
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►The last reference includes analogs for arithmetic in the complex plane .
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►For error measures for complex arithmetic see Olver (1983).
2: Bibliography O
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Error Analysis of Complex Arithmetic.
In Computational Aspects of Complex Analysis (Braunlage, 1982), H. Werner, L. Wuytack, E. Ng, and H. J. Bünger (Eds.),
NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., Vol. 102, pp. 279–292.
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3: 3.8 Nonlinear Equations
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►However, when the coefficients are all real, complex arithmetic can be avoided by the following iterative process.
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4: Bibliography S
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Algorithm 786: Multiple-precision complex arithmetic and functions.
ACM Trans. Math. Software 24 (4), pp. 359–367.
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5: Bibliography P
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Complex Interval Arithmetic and its Applications.
Mathematical Research, Vol. 105, Wiley-VCH Verlag Berlin GmbH, Berlin.
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6: 1.9 Calculus of a Complex Variable
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Arithmetic Operations
…7: Bibliography M
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8: 22.20 Methods of Computation
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§22.20(ii) Arithmetic-Geometric Mean
… ►Then as sequences , converge to a common limit , the arithmetic-geometric mean of . … ►The rate of convergence is similar to that for the arithmetic-geometric mean. … ►using the arithmetic-geometric mean. … ►Alternatively, Sala (1989) shows how to apply the arithmetic-geometric mean to compute . …9: 19.22 Quadratic Transformations
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►If or , then and are complex conjugates.
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§19.22(ii) Gauss’s Arithmetic-Geometric Mean (AGM)
►The AGM, , of two positive numbers and is defined in §19.8(i). …As , and converge quadratically to and 0, respectively, and converges to 0 faster than quadratically. … ►If or , then and are complex conjugates. …10: Bibliography Y
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The calculation of the Riemann zeta function in the complex domain.
USSR Comput. Math. and Math. Phys. 25 (2), pp. 111–119.
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Computation of the derivatives of the Riemann zeta-function in the complex domain.
USSR Comput. Math. and Math. Phys. 28 (4), pp. 115–124.
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Software for interval arithmetic: A reasonably portable package.
ACM Trans. Math. Software 5 (1), pp. 50–63.
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