It is a classical task in perturbation analysis to find norm bounds on the effect of a perturbation \(\Delta\) of a stochastic matrix \(G\) to its stationary distribution, i.e., to the unique norma…
GMRES-based iterative refinement in three precisions (GMRES-IR3), proposed by Carson and Higham in 2018, uses a low precision LU factorization to accelerate the solution of a linear system without …
We present a theory for general partial derivatives of matrix functions of the form , where is a matrix path of several variables. Building on results by Mathias [SIAM J. Matrix Anal. App…
We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically,…
Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analy…
We present a linear algebra formulation of backpropagation which allows the calculation of gradients by using a generically written “backslash” or Gaussian elimination on triangular systems of …
This is a further discussion of a previous work of the author on tensors with different rank and symmetric rank. We point out several obstructions towards extending a complex number example to the …
We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weig…
As a crucial first step towards finding the (approximate) common roots of a (possibly overdetermined) bivariate polynomial system of equations, the problem of determining an explicit numerical basi…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also int…