DirichletCharacter (Built-in Mathematica Symbol)

DirichletCharacter[k, j, n] gives the Dirichlet character \[Chi] {k, j} (n) with modulus k and index j.

Line Search Methods (Mathematica Tutorial)

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. ...

Special Functions (Mathematica Tutorial)

Mathematica includes all the common special functions of mathematical physics found in standard handbooks. Each of the various classes of functions is discussed in turn. One ...

KalmanEstimator (Built-in Mathematica Symbol)

KalmanEstimator[ss, {w, v}] constructs the Kalman estimator for the StateSpaceModel object ss with process and measurement noise covariance matrices w and v. ...

ProductLog (Built-in Mathematica Symbol)

ProductLog[z] gives the principal solution for w in z == w e^w. ProductLog[k, z] gives the k\[Null]^th solution.

Nonlinear PDEs (Mathematica Tutorial)

The general first-order nonlinear PDE for an unknown function u(x,y) is given by Here F is a function of uu(x,y), p ( ∂u(x,y) ) / ( ∂x ) , and q ( ∂u(x,y) ) / ( ∂y ) . The ...

EvaluationMonitor (Built-in Mathematica Symbol)

EvaluationMonitor is an option for various numerical computation and plotting functions that gives an expression to evaluate whenever functions derived from the input are ...

N (Built-in Mathematica Symbol)

N[expr] gives the numerical value of expr. N[expr, n] attempts to give a result with n-digit precision.

Test Problems (Mathematica Tutorial)

All the test problems presented in [MGH81] have been coded into Mathematica in the Optimization`UnconstrainedProblems` package. A data structure is used so that the problems ...

SingularValueList (Built-in Mathematica Symbol)

SingularValueList[m] gives a list of the nonzero singular values of a matrix m. SingularValueList[{m, a}] gives the generalized singular values of m with respect to a. ...