Use forward elimination to make the coefficient matrix, A, an upper triangular matrix, and then solve using back substitution, for a sample 2-by-2 system.
radius of a spherical planet
False position (linear interpolation) method of finding a root.
Bisection method of finding a root.
Quasi-Newton Method for Unconstrained Minimization using BFGS Update
Free Fall analytical solution (Chapra 2012 textbook Example 1.1)
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