Showing papers on "Divide-and-conquer eigenvalue algorithm published in 1969"
44 citations
TL;DR: In this paper, the authors derived robust estimates of amplification rates, wave speeds and sufficient conditions for linear stability for the manifold of solutions of the Orr-Sommerfeld problem governing parallel motion in the boundary layer and in round pipes.
Abstract: Rigorous estimates of amplification rates, wave speeds and sufficient conditions for linear stability are derived for the manifold of solutions of the Orr—Sommerfeld problem governing parallel motion in the boundary layer and in round pipes. The estimates for channel flow (part I) are improved and compared with numerical results for the neutral stability of Jeffery—Hamel flow.
38 citations
TL;DR: In this article, sets of simple matrices of order N are given, together with all of their eigenvalues and right eigenvectors, and simple rules for generating their inverses in the nonsingular cases.
Abstract: Sets of simple matrices of order N are given, together with all of their eigenvalues and right eigenvectors, and simple rules for generating their inverses in the nonsingular cases. In general, these matrices are nonsymmetric. They can have sets of double and triple roots. In each of these cases, two of the roots of the doublet or triplet can correspond to a single eigenvector. | The general form of the N X N matrix is :
25 citations
TL;DR: The bounds for the complex wave velocity c, determined by the Orr-Sommerfeld equation and the boundary conditions for channel flow, have been given by Joseph.
Abstract: Bounds for the complex wave velocity c , determined by the Orr-Sommerfeld equation and the boundary conditions for channel flow, have been given by Joseph (1968 a,b ). In these notes it is shown how two of Joseph's theorems can be uniformly improved.
16 citations
DOI•
01 Jan 1969
TL;DR: The final author version and the galley proof are versions of the publication after peer review and the final published version features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
14 citations
TL;DR: In this paper, a simple single-parametric representation for the solution of the inverse eigenvalue problem of degree n = 2 is given, by means of which the mathematical properties of some recently published methods for calculating force constants are investigated.
12 citations
11 citations
TL;DR: In this article, the generalized algebraic eigenvalue problem (A - lambda B)x = O arises in the use of the variation method in quantum mechanics, where, within the limitations of the computer word-length, the basis set used to expand the trial wave function is linearly dependent.
Abstract: : The generalized algebraic eigenvalue problem (A - lambda B)x = O arises in the use of the variation method in quantum mechanics. If, within the limitations of the computer word-length, the basis set used to expand the trial wave function is linearly dependent, the matrix B becomes singular. Three different algorithms designed to deal with this difficulty have been investigated, paying special attention to the problem of identifying which members of the basis set are effectively linearly dependent. The advantages and limitations of each method are discussed. (Author)
9 citations
5 citations