The efficient utilization of mixed-precision numerical linear algebra algorithms can offer
attractive acceleration to scientific computing applications. Especially with the hardware …

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 …

The BLAS-like Library Instantiation Software (BLIS) framework is a new infrastructure for
rapidly instantiating Basic Linear Algebra Subprograms (BLAS) functionality. Its fundamental …

Parallelizing dense matrix computations to distributed memory architectures is a well-
studied subject and generally considered to be among the best understood domains of …

The problem of learning long-term dependencies in sequences using Recurrent Neural
Networks (RNNs) is still a major challenge. Recent methods have been suggested to solve …

Summary The Gram–Schmidt process uses orthogonal projection to construct the A= QR
factorization of a matrix. When Q has linearly independent columns, the operator P= I− Q …

A fundamental problem when adding column pivoting to the Householder QR factorization is
that only about half of the computation can be cast in terms of high performing matrix-matrix …

Automated MRI (Magnetic Resonance Imaging) brain tumor segmentation is a difficult task
due to the variance and complexity of tumors. In this paper, a statistical structure analysis …

Linear Transformers have gained attention as efficient alternatives to standard Transformers,
but their performance in retrieval and long-context tasks has been limited. To address these …

A randomized algorithm for computing a so-called UTV factorization efficiently is presented.
Given a matrix A, the algorithm “randUTV” computes a factorization A= UTV*, where U and V …