V. Simoncini and E. Gallopoulos. Transfer functions and resolvent norm approximation of large matrices. Electronic Transactions on Numerical Analysis (ETNA), 7:190--201, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....can be simultaneously reduced to triangular form) We therefore look for other ways to efficiently evaluate or approximate liP(z) II for many different z. 3.1. Transfer function approach. The idea of writing pseudospectra in terms of transfer functions is not new. Simoncini and Gallopoulos [34] used a transfer func tion framework to rewrite most of the techniques used to approximate e pseudospectra of large matrices, yielding interesting comparisons as well as better understanding of the techniques. Hinrichsen and Kelb [17] investigated structured pseudospectra of a single matrix with ....

....the resolvent norm by the Arnoldi method; that is, they approximate II(A zI) lll2 by II(Hm zI) lll2 or by Crmin(tm Z[ where Hm is the square Hessenberg matrLx of dimension m n obtained from the Arnoldi process and Hm is the matrLx Hm augmented by an extra row. Simoncini and Gallopoulos [34] show that a better but more costly approximation is obtained by approximating II (A zI) 112 with IIV (A zI) Vm 112, where V m is the orthonor mal basis generated during the Arnoldi process. These techniques are not applicable to the polynomial eigenvalue problem of degree larger than one ....

V. SIMONCINI AND E. GALLOPOULOS, Transfer functions and resolvent norm approximation of large matrices, Electron. Trans. Numer. Anal., 7 (1998), pp. 190-201.

....Q( Gamma1 = I 0 ] A Gamma B) Gamma1 0 I : 3.10) The matrix Q( Gamma1 is often called the resolvent of Q( and is closely related to the transfer function for a time invariant linear system. The value of its norm for several is required when computing pseudospectra of Q( see [116], 129] and section 4.3) Next we obtain an explicit expression for the resolvent in terms of the eigenpairs of Q( First, we note that the equation Q( i )x i = 0 is equivalent to AOE i = i BOE i with OE i = x T i ; i x T i ] T and the eigenvalues of Q( and (A; B) coincide. If all the ....

V. Simoncini and E. Gallopoulos, Transfer functions and resolvent norm approximation of large matrices, Electronic Transactions on Numerical Analysis, 7 (1998), pp. 190--201.

....be simultaneously reduced to triangular form) We therefore look for other ways to efficiently evaluate or approximate kP (z) Gamma1 k for many different z. 3.1. Transfer function approach. The idea of writing pseudospectra in terms of transfer functions is not new. Simoncini and Gallopoulos [25] used a transfer function framework to rewrite most of the techniques used to approximate ffl pseudospectra of large matrices, yielding interesting comparisons as well as better understanding of the techniques. Hinrichsen and Kelb [10] investigated structured pseudospectra of a single matrix with ....

....that is, they approximate k(A Gamma zI) Gamma1 k 2 by k(Hm Gamma zI) Gamma1 k 2 or by oe min ( e Hm Gamma z e I) where Hm is the square Hessenberg matrix of dimension m n obtained from the Arnoldi process and e Hm is the matrix Hm augmented by an extra row. Simoncini and Gallopoulos [25] show that a better approximation is obtained by approximating k(A Gamma zI) Gamma1 k 2 with kV m (A GammazI) Gamma1 Vm 1 k 2 where Vm is the orthonormal basis generated during the Arnoldi process. These techniques are not applicable to the polynomial eigenvalue problem of degree larger ....

V. Simoncini and E. Gallopoulos. Transfer functions and resolvent norm approximation of large matrices. Electronic Transactions on Numerical Analysis, 7:190--201, 1998.

No context found.

V. Simoncini and E. Gallopoulos. Transfer functions and resolvent norm approximation of large matrices. Electronic Transactions on Numerical Analysis (ETNA), 7:190--201, 1998.

....of the pseudospectrum domain in order to reduce the number of points where oe min needs to be computed [3,7,8,14] Matrix based: Methods that attempt to reduce C oe min at each point. These include dense and sparse matrix techniques for the sequential or parallel evaluation of singular triplets [6,9,16,17,20,22,23,25]. See also [26] for a nice collection of on line resources related to this topic. In this paper we are primarily in domain based techniques for the following version of the pseudospectrum problem: Problem PSe: Given A 2 C and an ffl 0, compute the corresponding ffl pseudospectrum curve ....

....the SVD as the problem size increases. In particular, even using Cobra, the cost of computing pseudospectra becomes prohibitive for large matrices. One way to delay meeting this cost barrier is to use iterative methods [19,21] Another is to combine Cobra with estimators of the resolvent norm; see [23,25]. Indeed, there are many possibilities open for research but the nature of the problem suggests to us that the most effective approach would be a polyalgorithm that would try to extract all useful information about the input matrix and the nature of the computational resources and would then ....

V. Simoncini and E. Gallopoulos. Transfer functions and resolvent norm approximation of large matrices. Electronic Transactions on Numerical Analysis (ETNA), 7:190--201, 1998.

No context found.

V. Simoncini and E. Gallopoulos, Transfer functions and resolvent norm approximation of large matrices, Elect. Trans. Numer. Anal., 7 (1998), pp. 190-201.

No context found.

V. Simoncini and E. Gallopoulos, Transfer functions and resolvent norm approximation of large matrices, Elect. Trans. Numer. Anal., 7 (1998), pp. 190-201.

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