Mathematica incorporates the latest algorithms for solving industrial-scale linear systems, automatically switching between optimal dense and sparse algorithms—and handling ...

PseudoInverse[m] finds the pseudoinverse of a rectangular matrix.

There are often many different ways to write the same algebraic expression. As one example, the expression (1+x)^2 can be written as 1+2x+x^2. Mathematica provides a large ...

Even with "Newton methods" where the local model is based on the actual Hessian, unless you are close to a root or minimum, the model step may not bring you any closer to the ...

"Gauss–Newton" and "conjugate gradient" methods use derivatives. When Mathematica cannot compute symbolic derivatives, finite differences will be used. Computing derivatives ...

When derivatives cannot be computed symbolically, "Newton's" method will be used, but with a finite difference approximation to the Jacobian. This can have costs in terms of ...

Mathematica has a collection of commands that do unconstrained optimization (FindMinimum and FindMaximum) and solve nonlinear equations (FindRoot) and nonlinear fitting ...

ChanVeseBinarize[image] finds a two-level segmentation of image by computing optimal contours around regions of consistent intensity in image.ChanVeseBinarize[image, marker] ...

IsolatingInterval[a] gives a rational isolating interval for the algebraic number a.IsolatingInterval[a, dx] gives an isolating interval of width at most dx.

MaxExtraConditions is an option to Solve and related functions that specifies how many extra equational conditions on continuous parameters to allow in solutions that are ...