Efforts to understand the generalization mystery in deep learning have led to the belief that
gradient-based optimization induces a form of implicit regularization, a bias towards models …

We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in
numerical simulation and control. The structure is ideal for automated network-based …

We investigate the singular value decomposition (SVD) of a rectangular matrix of functions
that are analytic on an annulus that includes at least the unit circle. Such matrices occur, eg …

In many large scale scientific or engineering computations, ranging from computing the
frequency response of a circuit to the earthquake response of a buildingto the energy levels …

In the last 30 years, differential-algebraic equations have become a widely accepted tool for
the modeling and simulation of constrained dynamical systems in numerous applications …

For the low-rank approximation of time-dependent data matrices and of solutions to matrix
differential equations, an increment-based computational approach is proposed and …

Inverse eigenvalue problems arise in a remarkable variety of applications and associated
with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of …

An analytic parahermitian matrix admits in almost all cases an eigenvalue decomposition
(EVD) with analytic eigenvalues and eigenvectors. We have previously defined a discrete …

A collection of inverse eigenvalue problems are identified and classified according to their
characteristics. Current developments in both the theoretic and the algorithmic aspects are …

This book is designed to be used by mathematicians, engineers, and computer scientists as
a graduate-level introduction to numerical analysis and its methods. Readers are expected …