ON THE CONVERGENCE OF A NEW RAYLEIGH QUOTIENT METHOD WITH APPLICATIONS TO LARGE EIGENPROBLEMS [PDF]
, 2008 . In this paper we propose a variant of the Rayleigh quotient method to compute an eigenvalue and corresponding eigenvectors of a matrix. It is based on the observation that eigenvectors of a matrix with eigenvalue zero are also singular vectors ...
D. P. Oleary Y, G. W. Stewart Z
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If A Matrix Has Only A Single Eigenvalue How Sensitive Is This Eigenvalue? II [PDF]
, 1998 . For matrices with a single eigenvalue the sensitivity of the eigenvalue to perturbations in the matrix is analyzed. Simple bounds are derived that separate the influence of the index on the eigenvalue sensitivity from the influence of the non-normality.
Grace E. Cho, C. F. Ipsen, Ilse
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If A Matrix Has Only A Single Eigenvalue How Sensitive Is This Eigenvalue? [PDF]
, 1997 . For matrices with a single eigenvalue we analyse the sensitivity of the eigenvalue to perturbations in the matrix. We derive a closed form result that is similar in spirit to an analytical result by Lidskii; improve a bound by Henrici; and express the ...
Grace E. Cho, Ilse C.F. Ipsen
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An Overview Of Relative sin Theta Theorems For Invariant Subspaces Of Complex Matrices [PDF]
, 2007 . Relative perturbation bounds for invariant subspaces of complex matrices are reviewed, with emphasis on bounding the sines of the largest principal angle between two subspaces, i.e. sin \Theta theorems.
Ilse C. F. Ipsen
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Relative Perturbation Bound for Invariant Subspaces of Indefinite Hermitian Matrix [PDF]
, 1998 We give bound for the perturbations of invariant subspaces of nonsingular indefinite Hermitian matrix H under relative additive perturbations of H. Such perturbations include the case when the elements of H are known up to some relative tolerance.
Ivan Slapnicar, Ninoslav Truhar
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Absolute And Relative Perturbation Bounds For Invariant Subspaces Of Matrices [PDF]
, 1998 . Absolute and relative perturbation bounds are derived for angles between invariant subspaces of complex square matrices, in the two-norm and in the Frobenius norm.
Ilse C. F. Ipsen
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ON SPACES OF MATRICES WITH A BOUNDED NUMBER OF EIGENVALUES [PDF]
, 2008 Dedicated to Hans Schneider on the occasion of his seventieth birthday Abstract. The following problem, originally proposed by Omladic and Semrl [Linear Algebra Appl., 249:29{46 (1996)], is considered. Let k and n be positive integers such that k < n.
Nizar Radwan, Raphael Loewy
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The Spread of the Spectrum of a Graph [PDF]
, 2007 Upper and lower bounds are obtained for the spread 1 \Gamma n of the eigenvalues 1 2 \Delta \Delta \Delta n of the adjacency matrix of a simple graph.
Daniel Hershkowitz +3 more
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A Note On The Field Of Values Of Non-Normal Matrices [PDF]
, 2007 . It is shown that the distance from zero of the field of values of a matrix A depends on how large the departure from normality is compared to the distance from the zero of the field of values of the normal part of A.
Ilse C. F. Ipsen
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Minimum trace norm of real symmetric and Hermitian matrices with zero diagonal
Special MatricesWe establish tight lower bounds for the trace norm (‖⋅‖1)\left(\Vert \cdot {\Vert }_{1}) of real symmetric and Hermitian matrices with zero diagonal entries in terms of their entrywise L1{L}^{1}-norms (‖⋅‖(1))\left(\Vert \cdot {\Vert }_{\left(1)}).
Einollahzadeh Mostafa +1 more
doaj +1 more source