Fast Dense Numerical Linear Algebra

Mathematica 5 offers class-leading performance for dense numerical linear algebra--a key building block for numerical functionality. These performance increases affect uses such as data analysis, numerical differential equation solving, optimization, and graphics. In most cases, computational speed now matches or exceeds Fortran or MATLAB code, while maintaining Mathematica's breadth of usability.

These graphs show timing comparisons of Mathematica 4.2 and Mathematica 5. All timings are the average of four trials on the same matrix of random real numbers on a 1.8 GHz Pentium 4 machine with Windows XP and 1 gigabyte of RAM. For example, the same 1000 x 1000 matrix is used for each trial in each comparison.

Mathematica 5 also takes advantage of multiple processors for a range of numerical operations on those operating systems such as Linux, Windows, and HP-UX that support this multithreaded capability.

As computations become larger, maximum efficiency can be gained from multiple processors.

		Documentation from The Mathematica Book Solving Linear Systems Matrix Inversion Basic Matrix Operations Multiplying Vectors and Matrices
		Advanced Documentation Linear Algebra
		Other Links gigaNumerics (Key Technology)