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Nonlinear Equations
Published in Jeffery J. Leader, Numerical Analysis and Scientific Computation, 2022
Floating point numbers in the form (mantissa)×(base)exponent incorporate trade-offs made in deciding that, say, double precision numbers have 52 bit mantissas with 11 bit exponents, as opposed to the 46 bit mantissas and 17 bit exponents that would have resulted from a straight-forward doubling of the significand from single precision. Discuss the trade-offs between these two possible versions of double precision.How many bits would be used for a quadruple precision value? How many words does that correspond to? How would you suggest the bits be distributed (sign, exponent, mantissa)? Look up the IEEE 754 binary128 standard for quadruple precision and compare it to your suggested format.Discuss and compare the different possibilities suggested for half precision.
Numerical Methods for Use in Preparing High-Quality Statistical Tables
Published in Donald B. Owen, Subir Ghosh, William R. Schucany, William B. Smith, Statistics of Quality, 2020
Morgan C. Wang, William J. Kennedy
Thus, simply computing in extended precision is not a way to guarantee any prescribed level of accuracy in end results. In other words, computing the same answers using single precision, and double precision, and quadruple precision and … precision does not guarantee that the answers are correct to within any finite prescribed epsilon.
Edge effects in elastic and piezoelectric laminated panels under thermal loading
Published in Journal of Thermal Stresses, 2018
Numerical results are presented for (a) a cross-ply composite panel made of graphite/epoxy (Gr/Ep), (b) a sandwich panel, and (c) a hybrid panel under thermal loading. The lay-ups of these laminates are shown in Figure 2, and the material properties of various layers are presented in Table 1. The span to thickness ratio () of all the panels is taken as 5. The present formulation is validated by comparing the results against the 3D piezothermoelasticity based exact solution for the simply supported composite and hybrid panels under thermal loading. Further, the free edge effects in elastic and hybrid laminates under uniform and thermal gradient loading are studied. The effect of pyroelectric coupling on the free edge stress field is examined. The feasibility of controlling the free edge thermal stress field by applying appropriate electric potential is also investigated. The numerical results are obtained using the quadruple precision (128 bit) program. The results for panels with simply supported and free edge boundary conditions at the edges are normalized as follows: