The authors present an algorithm for order reduction of linear time invariant dynamic systems using the combined advantages of the eigen spectrum analysis and the error minimization by particle swarm optimization technique. Pole centroid and system stiffness of both original and reduced order systems remain same in this method to determine the poles, whereas zeros are synthesized by minimizing ...

Internet Electron. J. Mol. Des. 2003, 1, 000–000 Abstract Motivation. A QSPR analysis has been conducted on the half-wave reduction potential (E1/2) of a diverse set of organic compounds by means of principal component regression (PCR) and principal component-artificial neural network (PC-ANN) modeling method. Genetic algorithm was employed as a factor selection procedure for both modeling meth...

Eigenvalue analysis plays an important role in understanding physical phenomena. However, if one deals with strongly nonnormal matrices or operators, the eigen-values alone may not tell the full story. A popular tool which can be useful to get more insight in the reliability or sensitivity of eigenvalues is "-pseudospectra. Apart from "-pseudospectra we consider other tools which might help to ...

We present a method allowing a signiicant speed-up of the eigen-detection method (detection based on principle component analysis). We derive a formula for an upper bound on the class-conditional probability (or, equivalently, a lower bound on the Mahalanobis distance) on which detection is based. Often, the lower bound of Mahalanobis distance (MD) reaches a preset threshold after computation o...

The spherical harmonics Y l m form a basis of the vector space V (of dimensions 2l + 1) of the eigen functions of the Laplacian on the sphere, with eigen value λl = −l (l+ 1). Here we show the existence of an other basis Φj for V, where Φj(X) ≡ (X · Nj), the l power of the scalar product of the current point with a specific null vector Nj . This very simple formulation makes calculations very e...