Face recognition and identification are very important applications in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization matrix PCA methods can be difficult implement. Moreover, tensorial a natural choice, due mere structure databases, for example case color images. Nevertheless, even though various authors proposed factorization str...

Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications medical detection and location bodily tumors since it affordable non-invasive method, which aims recover internal conductivity body using voltage measuremen...

We consider algorithms for going from a “full” matrix to a condensed “band bidiagonal” form using orthogonal transformations. We use the framework of “algorithms by tiles”. Within this framework, we study: (i) the tiled bidiagonalization algorithm BiDiag, which is a tiled version of the standard scalar bidiagonalization algorithm; and (ii) the R-bidiagonalization algorithm R-BiDiag, which is a ...

The harmonic Lanczos bidiagonalization method can be used to compute the smallest singular triplets of a large matrix A. We prove that for good enough projection subspaces harmonic Ritz values converge if the columns of A are strongly linearly independent. On the other hand, harmonic Ritz values may miss some desired singular values when the columns of A are almost linearly dependent. Furthermo...

We extend the Golub-Kahan algorithm for computing the singular value decomposition of bidiagonal matrices to triangular matrices R. Our algorithm avoids the explicit formation of R T R or RRT. We derive a relation between left and right singular vectors of triangular matrices and use it to prove monotonic convergence of singular values and singular vectors. The convergence rate for singular val...

The conference dinner will take place in Café Campus behind the Mathematics Building on the campus of TU Berlin. We discuss a general framework for sensitivity and perturbation analysis of polynomial eigen-value problem. More specifically, we discuss first order variations of simple eigenvalues of matrix polynomials, determine the gradients and present a general definition of condition number o...

New restarted Lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented. Restarting is carried out by augmentation of Krylov subspaces that arise naturally in the standard Lanczos bidiagonalization method. The augmenting vectors are associated with certain Ritz or harmonic Ritz vectors. Computed examples show the ne...

Many applications require the solution of large nonsymmetric linear systems with multiple right-hand sides. Instead of applying an iterative method to each of these systems individually, it is often more eecient to use a block version of the method that generates iterates for all the systems simultaneously. In this paper, we propose block versions of Galerkin/minimal residual pair of bidiagonal...

The partial least squares (PLS) method computes a sequence of approximate solutions xk ∈ Kk(AA,A b), k = 1, 2, . . . , to the least squares problem minx ‖Ax− b‖2. If carried out to completion, the method always terminates with the pseudoinverse solution x† = A†b. Two direct PLS algorithms are analyzed. The first uses the Golub–Kahan Householder algorithm for reducing A to upper bidiagonal form....