Finding the spectral radius of a large sparse non-negative matrix

An always convergent method for finding the spectral radius of an irreducible non-negative matrix

An always convergent method is used to calculate the spectral radius of an irreducible non-negative matrix. The method is an adaptation of a method of Collatz (1942), and has similarities to both the power method and the inverse power method. For large matrices it is faster than the eig routine in Matlab. Special attention is paid to the step-by-step improvement of the bounds and the subsequent...

A Method for Parallel Non-negative Sparse Large Matrix Factorization

This paper proposes parallel methods of non-negative sparse large matrix factorization. The described methods are tested and compared on large matrices processing.

Derivatives of the spectral radius as a function of non - negative matrix elements

Random evolutions and the spectral radius of a non - negative matrix

1. Introduction and summary. This paper offers yet another example of what probability theory can do for analysis. Using a Feynman-Kac formula derived in the theory of random evolutions (51, we find an expression (1) for the spectral radius r(A) of a finite square non-negative matrix A. This expression makes it very easy to study how r(A) behaves as a function of the diagonal elements of A. Kac...

Sparse Non-negative Matrix Language Modeling

We present Sparse Non-negative Matrix (SNM) estimation, a novel probability estimation technique for language modeling that can efficiently incorporate arbitrary features. We evaluate SNM language models on two corpora: the One Billion Word Benchmark and a subset of the LDC English Gigaword corpus. Results show that SNM language models trained with n-gram features are a close match for the well...