The transformation was designed to approximate a gamma of about 2.2, but with a linear portion near zero to avoid having an infinite slope at " K " = 0, which can cause numerical problems.
12.
Fifth-and sixth-order curves are sometimes useful, especially for obtaining continuous higher order derivatives, but curves of higher orders are practically never used because they lead to internal numerical problems and tend to require disproportionately large calculation times.
13.
He has used these first generation systems extensively to solve both deterministic numerical problems such as matrix inversion and matrix eigenvalue problems, non-linear algebraic equations, and linear optimization problems as well as probabilistic problems such as Rayleigh-Pearson Random Walk related problems.
14.
For lateration compared to angulation, the numerical problems compare, but the technical problem is more challenging with angular measurements, as angles require two measures per position when using optical or electronic means for measuring phase differences instead of counting wave cycles.
15.
Once again, the case of the ray passing through a vertex may pose numerical problems in finite precision arithmetics : for two sides adjacent to the same vertex the straightforward computation of the intersection with a ray may not give the vertex in both cases.
16.
"We made our point the last time, the point being that we have developed a tool, using chess as a model, to solve complex numerical problems, " said C . J . Tan, the manager of IBM's Deep Blue project, which began in 1989 . " This match is just a competition ."
17.
Near multiples of 180? care is needed to avoid numerical problems : in extracting the angle, a two-argument arctangent with atan2 ( sin ?, cos ? ) equal to ? avoids the insensitivity of arccosine; and in computing the axis magnitude in order to force unit magnitude, a brute-force approach can lose accuracy through underflow.
18.
Because is then large ( approaching, half the circumference ) a small error is often not a major concern in this unusual case ( although there are other great-circle distance formulas that avoid this problem ) . ( The formula above is sometimes written in terms of the arctangent function, but this suffers from similar numerical problems near = 1 .)
