Description
Chair: Pasqua D'Ambra
We address the solution of large-scale nonlinear least-squares problems by stochastic Gauss-Newton methods combined with a line-search strategy. The algorithms proposed have per-iteration computational complexity lower than classical deterministic methods, due to the employment of random models inspired by randomized linear algebra tools. Under suitable assumptions, the stochastic...
The randomized singular value decomposition proposed in [1] has certainly become one of the most well-established randomization-based algorithms in numerical linear algebra. The key ingredient of the entire procedure is the computation of a subspace which is close to the column space of the target matrix $\mathbf{A}$ up to a certain probabilistic confidence. In our work [2] we propose a...
Singular value decomposition (SVD) is a fundamental tool in data analysis and machine learning. Starting from the Stewart’s QLP decomposition [1], we propose an innovative Deep-QLP decomposition algorithm for efficiently computing an approximate Singular Value Decomposition (SVD) based on the preliminary work in [2]. Given a specified tolerance $\tau$, the algorithm automatically computes a...
We present a comprehensive matrix perturbation analysis of methods for extracting singular value from approximate subspaces. Given (orthonormal) approximations $\tilde{U}$ and $\tilde{V}$ to the left and right subspaces spanned by the leading singular vectors of a matrix A, we discuss methods to approximate the leading singular values of A and study their accuracy. In particular, we focus our...
The Perron-Frobenius theory was extended to multiplicative matrix semigroups relatively recently and has found many applications to synchronizing automata, nonhomogeneous Markov chains, linear dynamical systems, graphs, etc. This theory connects the spectral and combinatiorial properties of semigroups of nonnegative matrices. In particular, the concept of primitivity is especially important....
