数值计算与计算机应用 1980, 1(3 ) 181-192 DOI:     ISSN: 1000-3266 CN: 11-2124/TP

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关于科学计算用数字电子计算机的字长与速度、内存的匹配关系的讨论

周毓麟

摘要

对适合于科学计算用的数字电子计算机的字长的选取问题,实质上是个舍入误差积累的估计问题。对于一般的计算问题进行舍入误差积累的估计是个非常复杂的问题.舍入误差的积累不仅依赖于具体问题本身,依赖于问题中所含的参数,甚至于还依赖于问题

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A DISCUSSION ON THE MATCHING RELATIONS AMONG THE WORD LENGTH,SPEED AND MEMORY SPACE OF DIGITAL ELECTRONIC COMPUTER FOR THE USE OF SCIENTIFIC CALCULATION

Zhou Yu-lin

Abstract:

As usual, the subtraction has more influence in the loss of the number of effectivedigits. In this paper an abstract probability model is constructed for the statisticalestimation of the accumulation of rounding errors. The formula S_2-S_1=Δm+(1/2)log_2(T_2V_2/T_1V_1)+1/(2N)log_2(C_2/C_1),which deseribes the matching relation among word lengh S, speed V and memory spaceC of the computer is derived, where T denotes the time of the calculation for a certainproblem, Δm≥0, N=1,2,3. By taking one computer as reference, the above formula canbe used to consider the relationship for a new computer. Some other formulae of thematching relations are obtained.

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