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It is thought that the totient valence function N_phi(m)>=2, i.e., if there is an n such that phi(n)=m, then there are at least two solutions n. This assertion is called ...

A differential evolution method used to minimize functions of real variables. Evolution strategies are significantly faster at numerical optimization than traditional genetic ...

The study of groups. Gauss developed but did not publish parts of the mathematics of group theory, but Galois is generally considered to have been the first to develop the ...

Legendre-Gauss quadrature is a numerical integration method also called "the" Gaussian quadrature or Legendre quadrature. A Gaussian quadrature over the interval [-1,1] with ...

A prime factorization algorithm which uses residues produced in the continued fraction of sqrt(mN) for some suitably chosen m to obtain a square number. The algorithm solves ...

An indicial equation, also called a characteristic equation, is a recurrence equation obtained during application of the Frobenius method of solving a second-order ordinary ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

Maximum likelihood, also called the maximum likelihood method, is the procedure of finding the value of one or more parameters for a given statistic which makes the known ...

A theory of constructing initial conditions that provides safe convergence of a numerical root-finding algorithm for an equation f(z)=0. Point estimation theory treats ...

If one solution (y_1) to a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0 (1) is known, the other (y_2) may be found using the so-called reduction of ...