Related papers: Efficient initials for computing maximal eigenpair
We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…
Sequentially solving similar optimization problems under strict runtime constraints is essential for many applications, such as robot control, autonomous driving, and portfolio management. The performance of local optimization methods in…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
In the construction of low-rank matrix approximation and maximum element search it is effective to use maxvol algorithm. Nevertheless, even in the case of rank 1 approximation the algorithm does not always converge to the maximum matrix…
We analyze the stability of a class of eigensolvers that target interior eigenvalues with rational filters. We show that subspace iteration with a rational filter is robust even when an eigenvalue is near a filter's pole. These dangerous…
This paper describes an algorithm for the computation of FIRST and FOLLOW sets for use with feature-theoretic grammars in which the value of the sets consists of pairs of feature-theoretic categories. The algorithm preserves as much…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
The properties of the first (largest) eigenvalue and its eigenvector (first eigenvector) are investigated for large sparse random symmetric matrices that are characterized by bimodal degree distributions. In principle, one should be able to…
We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
Although deep learning based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance are not entirely understood from a mathematical point of view. Recently,…
This paper proposes an efficient method for computing partial eigenvalues of large sparse matrices what can be called the inexact inverse power method (IIPM). It is similar to the inexact Rayleigh quotient method and inexact Jacobi-Davidson…
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…
The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of…
We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a…
It is typical for a machine learning system to have numerous hyperparameters that affect its learning rate and prediction quality. Finding a good combination of the hyperparameters is, however, a challenging job. This is mainly because…
Gaussian processes are a versatile probabilistic machine learning model whose effectiveness often depends on good hyperparameters, which are typically learned by maximising the marginal likelihood. In this work, we consider iterative…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…