نتایج جستجو برای: right eigenvalue
تعداد نتایج: 297488 فیلتر نتایج به سال:
We examine the eigenstructure of generalized isosceles triangles and explore the possibilities of analytic solutions to the general eigenvalue problem in other triangles. Starting with work based off of Brian McCartin’s paper on equilateral triangles, we first explore the existence of analytic solutions within the space of all isosceles triangles. We find that this method only leads to consiste...
By making use of Janak’s interpolation in the Kohn-Sham method, together with an explicit and differentiable functional of the density for the exchange-correlation energy, like LDA or GGA, the second derivative of the energy with respect to the number of electrons, N, is evaluated from the derivative of the highest occupied molecular orbital (HOMO) with respect to N (left derivative), or from t...
We prove that for a right linear bounded normal operator on a quaternionic Hilbert space (quaternionic bounded normal operator) the norm and the numerical radius are equal. As a consequence of this result we give a new proof of the known fact that a non zero quaternionic compact normal operator has a non zero right eigenvalue. Using this we give a new proof of the spectral theorem for quaternio...
The total least squares (TLS) method is a successful approach for linear problems if both the system matrix and the right hand side are contaminated by some noise. For ill-posed TLS problems Renaut and Guo [SIAM J. Matrix Anal. Appl., 26 (2005), pp. 457 476] suggested an iterative method which is based on a sequence of linear eigenvalue problems. Here we analyze this method carefully, and we ac...
where A(x) = Ai(x) is the Airy function. (See [5], [11] for recent reviews.) Typically these results are proved by first establishing that for finite N the distribution of the right-most particle is the Fredholm determinant of an operator KN . The limit theorem then follows once one proves KN → KAiry in trace norm. The classic example is the finite N Gaussian Unitary Ensemble (GUE) where KN is ...
In this paper we obtain formulas for the left and right eigenvectors and minimal bases of some families of Fiedler-like linearizations of square matrix polynomials. In particular, for the families of Fiedler pencils, generalized Fiedler pencils, and Fiedler pencils with repetition. These formulas allow us to relate the eigenvectors and minimal bases of the linearizations with the ones of the po...
The solution to a general Sylvester equation AX−XB = GF ∗ with a low rank righthand side is analyzed quantitatively through Low-rank Alternating-DirectionalImplicit method (LR-ADI) with exact shifts. New bounds and perturbation bounds on X are obtained. A distinguished feature of these bounds is that they reflect the interplay between the eigenvalue decompositions of A and B and the right-hand ...
A class of linear operators L+λI between suitable function spaces is considered, when 0 is an eigenvalue of L with constant eigenfunctions. It is proved that L + λI satisfies a strong maximum principle when λ belongs to a suitable pointed left-neighborhood of 0, and satisfies a strong uniform antimaximum principle when λ belongs to a suitable pointed right-neighborhood of 0. Applications are gi...
In [1] and [2], Bernstein and Reznikov have introduced a new way of estimating the coefficients in the spectral expansion of φ2, where φ is a Maass cusp of norm 1 on a quotient Y = Γ\H of the Poincaré upper half-plane with finite volume. The question of obtaining the precise exponential decay of those coefficients had been posed by Selberg, and first solved by Good [5] (for holomorphic forms) a...
Given a pair of matrices and starting vectors, we present a procedure to generate the biorthonormal basis of the second-order right and left Krylov subspaces. The application is to solve the large-scale quadratic eigenvalue problems via oblique projection technique. This method can take full advantage of the sparseness of large-scale system as well as the superior convergence behavior of Krylov...
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