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1: 27.17 Other Applications

… ►Congruences are used in constructing perpetual calendars, splicing telephone cables, scheduling round-robin tournaments, devising systematic methods for storing computer files, and generating pseudorandom numbers. … ►Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.

2: Bibliography S

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Automatic computing methods for special functions. III. The sine, cosine, exponential integrals, and related functions. J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 291–311.

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Notes:

Includes Fortran code, maximum accuracy 18S.

External Links:

MathReview (Martin E. Price), ZentralBlatt

Referenced by:

§6.21(ii).

Encodings:

BibTeX

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3: 9.19 Approximations

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Corless et al. (1992) describe a method of approximation based on subdividing $ℂ$ into a triangular mesh, with values of $\mathrm{Ai}\left(z\right)$, ${\mathrm{Ai}}^{\prime }\left(z\right)$ stored at the nodes. $\mathrm{Ai}\left(z\right)$ and ${\mathrm{Ai}}^{\prime }\left(z\right)$ are then computed from Taylor-series expansions centered at one of the nearest nodes. The Taylor coefficients are generated by recursion, starting from the stored values of $\mathrm{Ai}\left(z\right)$, ${\mathrm{Ai}}^{\prime }\left(z\right)$ at the node. Similarly for $\mathrm{Bi}\left(z\right)$, ${\mathrm{Bi}}^{\prime }\left(z\right)$.

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4: Philip J. Davis

… ►At that time John Todd was Chief of the Numerical Analysis Section of the Applied Mathematics Division and head of the Computation Laboratory that co-developed, with the NBS Electronic Computer Laboratory, the Standards Eastern Automatic Computer (SEAC), the first fully operational stored-program electronic digital computer in the United States. …

5: 3.2 Linear Algebra

… ►During this reduction process we store the multipliers ${\mathrm{\ell }}_{jk}$ that are used in each column to eliminate other elements in that column. …