When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...

A method like "Newton's" method chooses a step, but the validity of that step only goes as far as the Newton quadratic model for the function really reflects the function. ...

Mathematically, sufficient conditions for a local minimum of a smooth function are quite straightforward: x^* is a local minimum if ∇f(x^*)=0 and the Hessian ∇^2f(x^*) is ...

CycleGraph[n] gives the cycle graph with n vertices C_n.

Both CUDALink and OpenCLLink have a state-of-the-art memory manager that reduces the amount of memory allocation and transfer to the GPU. If used properly, the memory system ...

ArgMax[f, x] gives a position x_max at which f is maximized.ArgMax[f, {x, y, ...}] gives a position {x_max, y_max, ...} at which f is maximized.ArgMax[{f, cons}, {x, y, ...}] ...

Beta[a, b] gives the Euler beta function \[CapitalBeta](a, b). Beta[z, a, b] gives the incomplete beta function \[CapitalBeta]_z (a, b).

BooleanTable[bf] gives a list of truth values for all possible combinations of variable values supplied to the Boolean function bf.BooleanTable[expr, {a_1, a_2, ...}] gives a ...

Cos[z] gives the cosine of z.

FindArgMax[f, x] gives the position x_max of a local maximum of f.FindArgMax[f, {x, x_0}] gives the position x_max of a local maximum of f, found by a search starting from ...