We analyze transient growth due to the linear interaction between streaks and streamwise vortices. We obtain initial perturbations which give optimal initial and total energy growth, characterize the dependence of the dynamics on the initial distribution of perturbation energy, and compare with results from pseudospectra analysis.

We generalize -pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the -pseudospectra.

Pseudospectra were introduced as early as 1975 and became popular tool during the 1990s.In this paper, we give a new definition of pseudospectra by using QR decomposition. Some properties of pseduospectra are explored and an algorithm for the computation of pseduospectra is given.

If A is a square matrix with spectral radius less than 1 then A k 0 as k c, but the powers computed in finite precision arithmetic may or may not converge. We derive a sufficient condition for fl(Ak) 0 as k x) and a bound on [[fl(Ak)[[, both expressed in terms of the Jordan canonical form of A. Examples show that the results can be sharp. We show that the sufficient condition can be rephrased i...

A matrix is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set nondiagonalizable matrices measure zero, every limit matrices. We prove quantitative version this fact conjectured by E. B. Davies: for each , at least -close to one whose eigenvectors have condition number worst some depending only on n. further show that dependence δ cannot be improved any constan...

In the first part of this paper (Sections 2-4), the main concern is with the boundary of the pseudospectrum of a matrix polynomial and, particularly, with smoothness properties of the boundary. In the second part (Sections 5-8), results are obtained concerning the number of connected components of pseudospectra, as well as results concerning matrix polynomials with multiple eigenvalues, or the ...

Pseudospectra provide an analytical and graphical alternative for investigating nonnormal matrices and operators, give a quantitative estimate of departure from non-normality and give information about stability. In this paper, we prove that pseudospectral radius is sub-additive and sub-multiplicative for a commuting pair of matrices over the complex field, extending the same result for spectra...

Our goal, in this paper, is to study some equivalent deenitions of the pseudospectra of a closed linear operator. We start from two deenitions, one with strict inequality and the other with non-strict inequality. The rst deenition makes the pseudospectrum open and the second makes it closed. We will show the subtle diierence between these seemingly almost identical deenitions and the relations ...