Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

Mathematica provides functions for the aesthetic drawing of graphs. Algorithms implemented include spring embedding, spring-electrical embedding, high-dimensional embedding, ...

LayeredGraphPlot attempts to draw the vertices of a graph in a series of layers, placing dominant vertices at the top, and vertices lower in the hierarchy progressively ...

TreePlot lays out the vertices of a graph in a tree of successive layers, or a collection of trees. If the graph g is not a tree, TreePlot lays out its vertices on the basis ...

For minimization problems for which the objective function is a sum of squares, it is often advantageous to use the special structure of the problem. Time and effort can be ...

The utility functions FindMinimumPlot and FindRootPlot show search data for FindMinimum and FindRoot for one- and two-dimensional functions. They work with essentially the ...

There are many variants of quasi-Newton methods. In all of them, the idea is to base the matrix B_k in the quadratic model on an approximation of the Hessian matrix built up ...

All the functions FindMinimum, FindMaximum, and FindRoot take variable specifications of the same form. The function FindFit uses the same form for its parameter ...

When fitting models to data, it is often useful to analyze how well the model fits the data and how well the fitting meets the assumptions of the model. For a number of ...

OpenCLImplicitRender3D[poly, vars, r] ray traces the implicit surface poly = 0 as a function of vars with bound sphere of radius r.