By Edward Sang
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Extra resources for A new table of seven-place logarithms
N. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, 1996. 10. J. , 1994. 15 Use three-digit decimal chopped arithmetic with m = - 100 and M = 100 to construct examples for which are of great practical value. It appears to be necessary to evaluate a large number of sines and cosines if we wish to evaluate such a series, but this can be done cheaply by recursion. let sn = sinnx and cn = cosnx. You are allowed to use negative numbers. Examples can be constructed so that either one of the expressions cannot be formed in the arithmetic, or both can be formed but the values are different.
The residual provides a for the backward error analysis, namely, = -r. The residual r is connected to the error e by r = b - Az = Ax - Az = A(x - z) = Ae -1 or e = A r. A small residual r, hence a small may be perfectly satisfactory from the point of view of backward error analysis even when the corresponding error e is not small. 8. 11) We carry out the elimination process using three-digit chopped decimal arithmetic. 11) is easily found to be xl = 1 and x2 = -1. 166341. Thus, z is the solution of a problem very close to the one posed, even though it differs considerably from the solution x of the original problem.
3. W. Cody and W. , 1980. 4. J. Dongarra, J. Bunch, C. Moler, and G. Stewart, LINPACK Users’ Guide, SIAM, Philadelphia, 1979. 5. C. , 1968. 6. G. ,” in Constructive Aspects of the Fundamental Theorem of Algebra, B. Dejon and P. , Wiley, London, 1969. REFERENCES 29 7. D. Goldberg, “What every computer scientist should know about floating-point arithmetic,” ACM Computing Surveys, 23 (1991), pp. 5-48. 8. P. Henrici, Elements of Numerical Analysis, Wiley, New York, 1964. 9. N. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, 1996.
A new table of seven-place logarithms by Edward Sang