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Cheap Tricks in Applied Mathematics

GK Matrix Reduction
A variation of Gaussian reduction for algebras not closed under division (e.g. polynomials).

On Computing Sines and Cosines
Tables and cubic interpolation.

Bessel Function Calculations
How to generate a Taylor series expansion about some x0 > 0.

Solving Integrals using Differential Equations
A class of integrals with no closed form solutions satisfy differential equations.

Tri-diagonal Transition Matrix
Converting matrixes with complex eigenvalues to tri-diagonal form so as to reduce the number of operations for state vector models.

Polynomial Roots
Simultaneous solution using vector Newton-Rhapson.

Eigenvalues and Eigenvectors
Steepest descent and orthogonalization.

Computing Gradient and Hessian from Objective Values
Nonlinear Optimization.

Kalman Smoothing
A tutorial.

Kalman Smoothing via Auxiliary Outputs
Alternate solutions.

Adjoint Gradients for System Identification
Nonlinear optimization.

Single Most Likely Replacement Detection
Echo detection.

Nahi's Balanced Realization
System Identification.

Deconvolution and Wavelet Estimation