The harmonic block Arnoldi method can be used to find interior eigenpairs of large matrices. Given a target point or shift to which the needed interior eigenvalues are close, the desired interior eigenpairs are the eigenvalues nearest and the associated eigenvectors. However, it has been shown that the harmonic Ritz vectors may converge erratically and even may fail to do so. To do a better job...

For a symmetric linear compact resp. densely defined operator with inverse, expansion theorems in series of eigenvectors are known. The aim the present paper is to generalize known case corresponding operators without symmetry property. this, we replace set orthonormal by biorthonormal principal vectors simple eigenvalues general eigenvalues. results for property all new. Furthermore, if symmet...

In this paper, we consider a block Jacobi preconditioner and various deflation techniques applied in the Deflated Preconditioned Conjugate Gradient (DPCG) method for solving sparse system of linear equations derived from statistical mixed model that analyses simultaneously phenotypic pedigree information genotyped ungenotyped animals with Single Polymorphism Nucleotide genotypes animals. livest...

In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...

in this paper, the dual area vector of a closed dual spherical curve is kinematically generatedand the dual steineer vector of a motion are extensively studied by the methods of differential geometry.jacobi’s theorems, known for real curves, are investigated for closed dual curves. the closed trajectorysurfaces generated by an oriented line are fixed in a moving rigid body in ir3 , in which the...

Previously we have showed that the computation of vectors in and bases for the null space of a singular matrix can be accelerated based on additive preconditioning and aggregation. Now we incorporate these techniques into the inverse iteration for computing the eigenvectors and eigenspaces of a matrix, which are the null vectors and null spaces of the same matrix shifted by its eigenvalues. Acc...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

In this note, we study the n×n random Euclidean matrix whose entry (i, j) is equal to f(‖Xi−Xj‖) for some function f and the Xi’s are i.i.d. isotropic vectors inR. In the regime where n and p both grow to infinity and are proportional, we give some sufficient conditions for the empirical distribution of the eigenvalues to converge weakly. We illustrate our result on log-concave random vectors.

A procedure for determining determining a few of the largest singular values and corresponding singular vectors of large sparse matrices is presented. Equivalent eigensystems are solved using a technique originally proposed by Golub and Kent based on the computation of modiied moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel im...