CS&E Profile: Yousef Saad

Sparse matrix computations, parallel computation, eigenvalue problems, and nonlinear equations.

Doctorat d'Etat 1983, Applied Mathematics, University of Grenoble, France

Doctorat de Troisieme Cycle 1974, Applied Mathematics, Grenoble, France

B.S. 1970, Mathematics, Algeria

About

Professor Saad's research interests include sparse matrix computations, parallel algorithms, nonlinear equations, and eigenvalue problems. He received the University Institute of Technology's Distinguished Professor award in 2005.

Saad has authored or co-authored five books, 112 Journal articles, and more than 50 papers and book chapters. He also developed several widely used software packages, including SPARSKIT, and more recently pARMS, for solving sparse linear systems of equations. He is an editor for the Electronic Transactions of Numerical Analysis (ETNA) and the Journal of Numerical Linear Algebra with Applications. He has also served as an editor for several other journals.

Research

My research interests span the following areas: sparse matrix computations, parallel computation, nonlinear equations, eigenvalue problems, and partial differential equations. One of my main goals is to develop numerical and nonnumeric techniques for large sparse matrices (matrices whose majority of elements are zeros). In particular, I have developed a software package for sparse matrix computations called SPARSKIT. For several years, I have been interested in matrix eigenvalue problems and large linear systems of equations and have investigated a number of techniques for such problems, based on so-called Krylov subspace methods. One of the problems that many researchers in numerical linear algebra are currently struggling with is to develop "robust" iterative methods for solving linear systems of equations. In fact, one reason why there is some reluctance in using these methods in applied sciences is that their performance is not predictable. In contrast, direct solvers are used as "black boxes" and are quite reliable, although often more expensive. On the other hand, with the tremendous gains in computer speeds, three-dimensional models are gaining ground and iterative methods become mandatory for solving the resulting systems of equations because of their size. Thus, there is still an enormous amount of work to be done, and researchers in iterative methods will face some serious challenges in the near future as mathematical models become more complicated and yield harder problems to solve.

My second major interest is in parallel computing, including efficient parallel algorithms for solving sparse linear equations. A challenging problem in this area is to develop methods that achieve good scalable performance – meaning a performance that improves close to proportionally with the number of processors. Standard algorithms must then be redesigned completely to achieve reasonable scalability. We are working on designing a general-purpose parallel code called PSPARSLIB for solving general sparse linear systems. The code implements iterative methods and can reach excellent scalability in some cases.

To say a few words on my other interests, I have been working on eigenvalue problems as well as on Jacobian-free inexact Newton methods. In partial differential equations I am interested in parallel methods for solving parabolic equations. I also have an ongoing collaborative effort with a group in the Department of Chemical Engineering and Materials Science which involves very large eigenvalue problems. More recently I also started an effort funded by the National Science Foundation in collaboration with a group in Aerospace Engineering. The goal of this work is to simulate the movement of particles in fluids.