Small differences in initial conditions ( such as those due to rounding errors in numerical computation ) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.
42.
The initial proofs of the inequality in the pivotal cases " n " = 12 ( Godunova and Levin, 1976 ) and " n " = 23 ( Troesch, 1989 ) rely on numerical computations.
43.
Experience with numerical computation of fields in cavities led, after the war, to a Master of Engineering degree ( 1948 ) and the definitive publication on step discontinuities in radial transmission lines ( 1954 ).
44.
Wolfram Alpha, which was released on May 18, 2009, is based on Wolfram's earlier flagship product Wolfram Mathematica, a computational platform or toolkit that encompasses computer algebra, symbolic and numerical computation, visualization, and statistics capabilities.
45.
This choice is claimed to have advantages in numerical computations when " ? " is very close to zero and simplify formulas in some contexts, such as in the Bayesian inference of variables with multivariate normal distribution.
46.
The conventional method of finite element analysis involves converting the differential equation that governs the problem into a field variables rounds off the mathematical process, following which numerical computations can be used to solve real life engineering problems.
47.
Together with their students, Abelson and Sussman are combining techniques from numerical computation, symbolic algebra, and heuristic programming to develop programs that not only perform massive numerical computations, but that also interpret these computations and " discuss " the results in qualitative terms.
48.
Together with their students, Abelson and Sussman are combining techniques from numerical computation, symbolic algebra, and heuristic programming to develop programs that not only perform massive numerical computations, but that also interpret these computations and " discuss " the results in qualitative terms.
49.
This is because, with high-powered numerical computation, most problems can be attacked through linearization ( at least within a certain range . . . remember part of the value of linear methods is that many processes are well approximated by linear processes ).
50.
Modern calculations in quantum chemistry usually start from ( but ultimately go far beyond ) a molecular orbital rather than a valence bond approach, not because of any intrinsic superiority in the former but rather because the MO approach is more readily adapted to numerical computations.
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