For the iterative solution of large sparse linear systems we develop a theory for a family of augmented and deflated Krylov space solvers that are coordinate based in the sense that the given problem is transformed into one that is formulated in terms of the coordinates with respect to the augmented bases of the Krylov subspaces. Except for the augmentation, the basis is as usual generated by a...

Multibody motion segmentation is important in many computer vision tasks. One way to solve this problem is factorization. But practically segmentation is difficult since the shape interaction matrix is contaminated by noise. This paper presents a novel approach to robustly segment multiple moving objects by spectral clustering. We introduce two new affinity matrixes. One is based on the shape i...

The main cost of Gauss-Newton (GN) inversion of timedomain controlled-source electromagnetic (tCSEM) data is comprised of the multiple solutions of the forward problem and linear-algebraic operations using the Jacobian matrix. For large-scale 2.5D and 3D problems with multiple sources and receivers, this cost grows enormously for inversion algorithms using conventional finite-difference time-do...

The symmetric Lanczos method is commonly applied to reduce large-scale symmetric linear discrete ill-posed problems to small ones with a symmetric tridiagonal matrix. We investigate how quickly the nonnegative subdiagonal entries of this matrix decay to zero. Their fast decay to zero suggests that there is little benefit in expressing the solution of the discrete ill-posed problems in terms of ...

The paper presentes a numerically stable and general algorithm for identification and realization of a complete dynamic linear state space model, including the system order, for combined deterministic and stochastic systems from time series. A special property of this algorithm is that the innovations covariance matrix and the Markov parameters for the stochastic sub-system are determined direc...

In this note we present a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation exp(A)v and establish a priori and a posteriori error estimates. Several such approximations are considered. The main idea of these techniques is to approximately project the exponential operator onto a small Krylov subspace and carry out the resulting small exponential matr...

The topic of this paper is the convergence analysis of subspace gradient iterations for the simultaneous computation of a few of the smallest eigenvalues plus eigenvectors of a symmetric and positive definite matrix pair (A,M). The methods are based on subspace iterations for A−1M and use the Rayleigh-Ritz procedure for convergence acceleration. New sharp convergence estimates are proved by gen...

We provide a different perspective of the spectral division methods for block generalized Schur decompositions of matrix pairs. The new approach exposes more algebraic structures of the successive matrix pairs in the spectral division iterations and reveals some potential computational difficulties. We present modified algorithms to reduce the arithmetic cost by nearly 50%, remove inconsistency...

In this paper, we perform a complete asymptotic performance analysis of the stochastic approximation algorithm (denoted subspace network learning algorithm) derived from Oja's learning equation, in the case where the learning rate is constant and a large number of patterns is available. This algorithm drives the connection weight matrix W to an orthonormal basis of a dominant invariant subspace...

Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algori...