Transpose-free multiple Lanczos and its application in Padé approximation

Transpose-free Multiple Lanczos and Its Application in Padé Approximation

A transpose-free two-sided nonsymmetric Lanczos method is developed for multiple starting vectors on both the left and right. The method is mathematically equivalent to the two-sided methods without look-ahead or deflation steps, but avoids the use of the transpose of the system matrix. The method is applied to the computation of the matrix Padé approximation to a linear dynamical system. The r...

Transpose-free Matrix Pad e Via Lanczos Method

A transpose-free two-sided nonsymmetric Lanczos method is developed for multiple starting vectors on both the left and right. The method is applied to the computation of the matrix Pad e approximation to a linear dynamical system. The result is a method which can be labeled Transpose-Free Matrix Pad e Via Lanczos. The method is mathematically equivalent to the two-sided methods, but avoids the ...

On Padé Approximation of Some Practical Functions

Approximation-free running SVD and its application to motion detection

In different tasks such as adaptive background modelling, the Singular Value Decomposition (SVD) has to be applied in running fashion. Typically, this happens when the SVD is used in a sliding spatial or temporal data window. Each time the window moves on, the SVD should be calculated in the batch mode from scratch, or re-calculated using the previous solution. When the data matrix is relativel...

Robust Padé Approximation via SVD

Padé approximation is considered from the point of view of robust methods of numerical linear algebra, in particular the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors; a Matlab code is provided. The success of this algorithm suggests that...