Cheap Tricks in Applied Mathematics

GK Matrix Reduction (also in DVI and PDF format)
A variation of Gaussian reduction for algebras not closed under division (e.g. polynomials).

Bessel Function Calculations (also in DVI and PDF format)
How to generate a Taylor series expansion about some x0 > 0.

Solving Integrals using Differential Equations (also in DVI and PDF format)
A class of integrals with no closed form solutions satisfy differential equations.

Tri-diagonal Transition Matrix (also in DVI and PDF format)
Converting matrixes with complex eigenvalues to tri-diagonal form so as to reduce the number of operations for state vector models.

Polynomial Roots (also in DVI and PDF format)
Simultaneous solution using vector Newton-Rhapson.

Eigenvalues (also in DVI and PDF format)
Conjugate gradient solution.

Kalman Smoothing (also in DVI and PDF format)
A tutorial.

Kalman Smoothing via Auxiliary Outputs (also in DVI and PDF format)
Alternate solutions.

Single Most Likely Replacement Detection (also in DVI and PDF format)
Echo detection.