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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?"
That problem isn't unique to regula falsi: Other than bisection, all of the numerical equation-solving methods can have a slow-convergence or no-convergence problem under some conditions. Sometimes, Newton's method and the secant method diverge instead of converging – and often do so under the same conditions that slow regula falsi's convergence.
Can solve convex problems with arbitrary precision types. CPLEX: commercial: CVXPY: open source Python modeling language with support for SOCP. Supports open source and commercial solvers. CVXOPT: open source Convex solver with support for SOCP ECOS: open source SOCP solver optimized for embedded applications FICO Xpress: commercial: Gurobi ...
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
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
In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations.It is a popular method for solving the large matrix equations that arise in systems theory and control, [1] and can be formulated to construct solutions in a memory-efficient, factored form.
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If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.