Pole-Swapping Algorithms for the Eigenvalue Problem

Matrix eigenvalue problems arise in a wide variety of fields in science and engineering, so it is important to have reliable and efficient methods for solving them. Of the methods devised, bulge-chasing algorithms, such as the famous QR and QZ algorithms, are the most important. This book focuses on pole-swapping algorithms, a new class of methods that are generalizations of bulge-chasing algorithms and a bit faster and more accurate owing to their inherent flexibility. The pole-swapping theory developed by the authors sheds light on the functioning of the whole class of algorithms, including QR and QZ. The only book on the topic, Pole-Swapping Algorithms for the Eigenvalue Problem describes the state of the art on eigenvalue methods and provides an improved understanding and explanation of why these important algorithms work.

Daan Camps is a quantum computing and HPC engineer in the Advanced Technologies Group at the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory. He worked as a postdoctoral researcher in the Applied Mathematics and Computational Research Division at Lawrence Berkeley National Laboratory and as a Ph.D. researcher in computer science at KU Leuven. His research interests span numerical linear algebra with an emphasis on eigenvalue problems, quantum computing and algorithms, high performance computing, and machine learning.

Thomas Mach is a postdoctoral researcher at the University of Potsdam, Germany. He has worked at KU Leuven, NU Astana, Kent State University, and the Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg. His primary research interests are eigenvalue problems, structure matrices, ill-posed problems, and data assimilation.

Raf Vandebril is a professor at KU Leuven, Belgium. He has a passion for teaching, and his primary research interests link to numerical linear algebra and numerical analysis, with an emphasis on the design of fast algorithms for structured rank matrices and eigenvalue problems.

David S. Watkins is a professor emeritus of mathematics at Washington State University. He is the author or coauthor of four books and numerous research and expository papers in the field of matrix computations, with an emphasis on eigenvalue problems. He has also published in physics and chemistry journals on various topics, including ionospheric physics and nonlinear optics.