Constrained low-rank matrix approximations have been known for decades as powerful
linear dimensionality reduction techniques able to extract the information contained in large …

High-fidelity blood flow modelling is crucial for enhancing our understanding of
cardiovascular disease. Despite significant advances in computational and experimental …

Recent advances in efficient Transformers have exploited either the sparsity or low-rank
properties of attention matrices to reduce the computational and memory bottlenecks of …

Since the early 1980. the first author has taught a graduate course in numerical linear
algebra at MIT and Cornell. The alumni of this course, now numbering in the hundreds, have …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

Overparameterized neural networks generalize well but are expensive to train. Ideally, one
would like to reduce their computational cost while retaining their generalization benefits …

Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of
high-dimensional data as it automatically extracts sparse and meaningful features from a set …

A promising trend in deep learning replaces traditional feedforward networks with implicit
networks. Unlike traditional networks, implicit networks solve a fixed point equation to …

Missing data is a crucial issue when applying machine learning algorithms to real-world
datasets. Starting from the simple assumption that two batches extracted randomly from the …

Representation learning constructs low-dimensional representations to summarize essential
features of high-dimensional data. This learning problem is often approached by describing …