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The art gallery problem or museum problem is a well-studied visibility problem in computational geometry.It originates from the following real-world problem: "In an art gallery, what is the minimum number of guards who together can observe the whole gallery?"
When the errors on x are uncorrelated, the general expression simplifies to =, where = is the variance of k-th element of the x vector. Note that even though the errors on x may be uncorrelated, the errors on f are in general correlated; in other words, even if Σ x {\displaystyle {\boldsymbol {\Sigma }}^{x}} is a diagonal matrix, Σ f ...
The MacCormack method is well suited for nonlinear equations (Inviscid Burgers equation, Euler equations, etc.)The order of differencing can be reversed for the time step (i.e., forward/backward followed by backward/forward).
Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
n = 1 that yield a minimax approximation or bound for the closely related Q-function: Q(x) ≈ Q̃(x), Q(x) ≤ Q̃(x), or Q(x) ≥ Q̃(x) for x ≥ 0. The coefficients {( a n , b n )} N n = 1 for many variations of the exponential approximations and bounds up to N = 25 have been released to open access as a comprehensive dataset.
This alternative definition is significantly more widespread: machine epsilon is the difference between 1 and the next larger floating point number.This definition is used in language constants in Ada, C, C++, Fortran, MATLAB, Mathematica, Octave, Pascal, Python and Rust etc., and defined in textbooks like «Numerical Recipes» by Press et al.
GPOPS-II [3] is designed to solve multiple-phase optimal control problems of the following mathematical form (where is the number of phases): = ((), …, ()) subject to the dynamic constraints
An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967. [1] The method was reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, [2] which runs in provably polynomial time (() operations on L-bit numbers, where n is the number of variables and constants), and is also very ...