Arithmetic Complexity of Computations by Shmuel Winograd

By Shmuel Winograd

Makes a speciality of discovering the minimal variety of mathematics operations had to practice the computation and on discovering a greater set of rules while development is feasible. the writer concentrates on that classification of difficulties taken with computing a method of bilinear types.

Results that bring about functions within the region of sign processing are emphasised, on the grounds that (1) even a modest relief within the execution time of sign processing difficulties may have sensible importance; (2) leads to this sector are particularly new and are scattered in magazine articles; and (3) this emphasis exhibits the flavour of complexity of computation.

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1 shows the results of a typical cross section measurementin this transitiol region, where interferenceeffectsbetween the electromagnetic and the strong scattering amplitudes can appear. 0 i3 ’0 i3 ’ 4 6 8 IO . $ . x t, ,,( + + -05 4 Q aqf++ ’ +xtr’Y r;l + + Fig. la, b, c. pp scatteringin the Coulombinterferenceregion. ItI and vs. &. Opt. Th. = optical theorem[65 B 31. Kirillova et al. Eellettini et al. Foley et 01. Eartenev et al. , Duttonet al. 5 -L 0 Taylor et al. 03 I t -1 0 1 10 4 GeV/c - Fig.

Fig. 3 shows an exampleof cross sectionsin the diffraction region. The slope parameterb is shown in Fig. 4a which is taken from Ref. [71 A 21 and is partly basedon a compilation by Lasinski et al. Beyond2 GeV/c, b showsa slow increasewith momentum: this phenomenonis called the “shrinking of the diffraction pattern”. Carrigan [70 C l] has suggestedthat the diffraction region, as defined above, cannot be describedby Eq. At the CERN ISR this has beenfound’to be indeed the case[72 B 21. 1 GeV’ in future.

0. (1963). (19651. 84GeV/c Harting et aL(l965). 9 GeV/c 10-j’ 1o-32 t 10-33 Fig. 6. The pp differential cross section, g separating the various curves clearly one from the other. The behaviour near @=9W varies strongly with energy 10-34 1o-35 10-36 vs. sin 0:, thus IO S- 0 Foley et al. 0 Harting et al. A Orear et al. GeV2II32 n Cocconi et al. * Alloby et al. &7. The energy dependence of pp elastic scattering at fixed t; $- vs. p1 and vs. s. At highvalues offour-momentum transfer the energy dependencebecomesvery steep.

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