In this work we estimate rates of the linear transient growth of the perturbations of cellular flames governed by the Sivashinsky equation. The possibility and significance of such a growth was indicated earlier in both computational and analytical investigations. Numerical investigation of the norm of the resolvent of the linear operator associated with the Sivashinsky equation linearized in a...

In this paper a new approach for moving objects detection in video surveillance systems is proposed. It is based on iLBP (intensity local binary patterns) descriptor that combines the classic LBP (local binary patterns) and the multiple regressive pseudospectra model. The iLBP descriptor itself is considered together with computational algorithm that is based on the sign image representation. W...

Numerically computed spectra and pseudospectra are presented for the linear operator that governs the temporal evolution of infinitesimal perturbations of laminar flow in an infinite circular pipe at Reynolds numbers 1000, 3000 and 10 000. The spectra lie strictly inside the stable complex half-plane, but the pseudospectra protrude significantly into the unstable half-plane, reflecting the larg...

Pseudospectra of rectangular matrices vary continuously with the matrix entries, a feature that eigenvalues of these matrices do not have. Some properties of eigenvalues and pseudospectra of rectangular matrices are explored, and an efficient algorithm for the computation of pseudospectra is proposed. Applications are given in (square) eigenvalue computation (Lanczos iteration), square pseudosp...

Human sound localization results primarily from the processing of binaural differences in sound level and arrival time for locations in the horizontal plane (azimuth) and of spectral shape cues generated by the head and pinnae for positions in the vertical plane (elevation). The latter mechanism incorporates two processing stages: a spectral-to-spatial mapping stage and a binaural weighting sta...

We describe a parallel software tool intended for the quantiication of the sensitivity of eigenvalues to matrix perturbations of varying size: the spectral portrait shows a representation of the normwise "-pseudospectra of a matrix A. This requires to compute k(A ? zI) ?1 k 2 for all z in a discretized region of the complex plane. The method used for computing k(A ? zI) ?1 k 2 has to be reliabl...

For studying spectral properties of a non-normal matrix A ∈ Cn×n, information about its spectrum σ(A) alone is usually not enough. Effects of perturbations on σ(A) can be studied by computing ε-pseudospectra, that is the level-sets of the resolvent norm function g(z) = ‖(zI−A)‖2. The computation of ε-pseudospectra requires determining the smallest singular values σmin(zI − A) on for all z on a ...

The eld of values and pseudospectra are tools which yield insight into the spectral behavior of a matrix. For large sparse matrices, both sets can be eeciently computed using a Lanczos type method. Since both computations can be done in a natural parallel way, we have developed a package including Fortran and PVM routines. Experiments show that the PVM codes achieve excellent speed-ups and eeci...

c ©2001, 2008 by Kenneth Miller. This work is licensed under the Creative Commons AttributionNoncommercial-Share Alike 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. Current versions of all parts of this work can be fou...

It is well known that the zeros of a polynomial p are equal to the eigenvalues of the associated companion matrix A. In this paper we take a geometric view of the conditioning of these two problems and of the stability of algorithms for polynomial zerofinding. The -pseudozero setZ (p) is the set of zeros of all polynomials p̂ obtained by coefficientwise perturbations of p of size ≤ ; this is a s...