Optimized linear algebra (LA) libraries that are able to exploit the underlying hardware are always of interest in the high-performance computing community. The implementation of LA software has evolved along with computer architecture, while the specification remains unaltered almost from the beginning. It is important to differentiate between the specification of LA libraries and their implementation. Because LA libraries pursue high performance, the implementation for a given architecture needs to be optimized for it specifically. However, the type of operations included in the libraries, the input/output parameters, and the data types to be handled are common to all of them. This is why, while the specification remains constant, the implementation evolves with the creation of new architectures.

Developing Linear Algebra Codes on Modern Processors: Emerging Research and Opportunities presents the main characteristics of LA libraries, showing the differences between the standards for sparse and dense versions. It further explores relevant linear algebra problems and shows, in a clear and understandable way, how to solve them using different computer architectures. Covering topics such as programming models, batched computing, and distributed memory platforms, this premier reference source is an excellent resource for programmers, computer scientists, engineers, students and faculty of higher education, librarians, researchers, and academicians.

Coverage:

The many academic areas covered in this publication include, but are not limited to:

Architectures
Batched Computing
Dense Linear Algebra
Distributed Memory Platforms
H-Matrices
Human Brain Simulation
Linear Algebra
Parallelism
Programming Models
Sparse Linear Algebra

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Editor/Author Biographies

Sandra Catalán Pallarés received a B.Sc. degree in Computer Science from Universitat Jaume I (UJI) of Castellón (Spain) in 2012, and an M.Sc. degree in Intelligent Systems (2013), and Ph.D. in Computer Science (2018) from the same university. In 2018, she moved as a postdoctoral researcher to Barcelona Supercomputing Center to work on the project "Porting and Optimization of Math Libraries" in collaboration with Fujitsu. In 2019, she joined Universidad Complutense de Madrid where she is currently an Assistant Professor. Her current research is focused on energy saving on moderate-scale clusters and low-power processors, parallel algorithms for numerical linear algebra, and asymmetric architectures.

Pedro Valero-Lara is a Computer Scientist in the Programming Systems Group into the Advanced Computing Systems Research Section and Computer Science and Mathematics Division of Oak Ridge National Laboratory. Previously, he was a Sr. Research Engineer at Cray Scientific and Math Libraries group, where he led the efforts for LibSci-Acc library, the Cray library for scientific (BLAS and LAPACK) computing on accelerators. In Spain, he was the founder and lead of the "Linear Algebra and Math Libraries" group at Barcelona Supercomputing Center. His work is part of several reference software packages for scientific computing (Kokkos, Cray/HPE LibSci-Acc, NVIDIA cuSparse, PLASMA, among others). Pedro was awarded by the IEEE-CS Early Career Researcher Award for Excellence in HPC in 2020, the Juan de la Cierva Fellowship in 2018, FPI-CIEMAT scholarship in 2011 and Microsoft Imagine Cup in 2009.

Leonel Antonio Toledo Díaz is a senior researcher at Fundació i2cat who is focused on high performance computing using accelerators. His interests include visualization, AI, computer graphics, HPC, and parallel algorithms. He has also worked on using general-purpose graphics processors for high-performance graphics. Leonel received his Ph.D from Instituto Tecnológico de Estudios Superiores de Monterrey Campus Estado de México in 2014, where he was a full-time professor from 2012-16. He has devoted most of his research work to crowd simulation and visualization optimization. Currently he is performing research in holoportation and virtual reality environments.

Rocío Carratalá Sáez received a B.Sc. Degree in Computational Mathematics by Universitat Jaume I (UJI) of Castellón (Spain) in 2015, M.Sc. Degree in Parallel and Distributed Computing by Universitat Politècnica de València (Spain) in 2016, and Ph.D. in Computer Science by UJI in 2021 (awarded with a MECD-FPU grant). She is currently an assistant professor at Universidad de Valladolid (UVa) in the Department of Computer Science. Her main research interest is High Performance Computing, focused on the parallelization of linear algebra operations. She is also interested in educational research, and has been part of some publications that explore how to improve the undergraduate students HPC skills.

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