Martin Bruhl, 1996. A curve tracing algorithm for computing the pseudospectrum. BIT, 36(3): 441-454.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is a nonempty, open, arcwise connected subset of C. Given a point z in an open set C, a particular example of a domain is the component of z, which consists of all points that can be joined to z by a continuous path in [35] The following result is in essence well known (see for example [10]) Theorem 5.1 (Eigenvalues and components) Every component of the strict pseudospectrum of the matrix A contains an eigenvalue of A. Proof Suppose the set S is a component of the strict pseudospectrum that contains no eigenvalues of A. The function g attains its minimum on the compact set ....

M. Bruhl. A curve tracing algorithm for computing the pseudospectrum. BIT, 36:441-454, 1996.

.... on function G(x; y) s(x; y) The key ingredient is that the gradient rG(x; y) necessary for the Newton iteration, can be easily computed, since rG(x; y) v u) v u) where v; u are the right and left singular vectors corresponding to the smallest singular value of A zI, [6] and ; denote the real and imaginary parts respectively. This sweep is embarrassingly parallel: each correction can be carried out completely independently from all others. Furthermore, the sweep can be repeated so as to compute a number of contours, moving towards the spectrum of A. This ....

M. Br uhl. A curve tracing algorithm for computing the pseudospectrum. BIT 33, 3 (1996), 441-445.

....A) Both approaches are the subject of active research; see [15] for a comprehensive survey of recent e orts. The use of path following, a powerful tool in many areas of applied mathematics, in order to compute a single boundary curve (A) was suggested by Kostin in [8] It was M. Br uhl in [5] who presented an algorithm to that end and showed that signi cant savings can be achieved compared to GRID when seeking a small number of boundary curves. The key is that tracing a single boundary curve, drastically reduces the number of min evaluations. Bekas and Gallopoulos carried this work ....

....sharp turns or neighboring curves. In particular, parallelism was introduced by incorporating multiple, decoupled, corrections. More recently, D. Mezher and B. Philippe suggested PAT, a new path following method that reliably traces contours [13] Despite its advantages over the original method of [5], Cobra maintains two weaknesses of the path following approach vis a vis GRID. These are a) that in each run, a single boundary curve (A) is computed, b) that is closed. Therefore, only one curve is computed at a time and its disconnected components are not captured, at least in a single ....

[Article contains additional citation context not shown here]

M. Bruhl. A curve tracing algorithm for computing the pseudospectrum. BIT, 33(3):441-445, 1996.

....pseudospectra of A by those of the resulting Hessenberg matrix. They also approximate the field of values of A by that of the Hessenberg matrix. Any of the methods described here can be used for the computations with the Hessenberg matrix. An alternative to the grid approach is developed by Br uhl [5], for situations in which only a few ffl pseudospectra are required. He computes the boundary of ffl (A) for a given ffl by curve tracing techniques, using a prediction correction scheme in which the correction is determined by a Newton step. Finally, we mention that Ruhe [29] investigates ....

Martin Bršuhl. A curve tracing algorithm for computing the pseudospectrum. Manuscript. Submitted to BIT, October 1995. 13 pp.

No context found.

Martin Bruhl, 1996. A curve tracing algorithm for computing the pseudospectrum. BIT, 36(3): 441-454.

No context found.

M. Bruhl. A curve tracing algorithm for computing the pseudospectrum. BIT, 36:441-454, 1996.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC