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# Professor Awarded the 14th Leslie Fox Prize in Numerical Analysis

Assistant Professor of Mathematics Brian Sutton |

Randolph-Macon College Assistant Professor of Mathematics Brian Sutton, Ph.D., was awarded first place for one of the highest awards in the field of mathematics, the 14th Leslie Fox Prize in Numerical Analysis, for his research in applied mathematics. Dr. Sutton competed against five finalists from Britain, France, Belgium, China and the United States. Each finalist gave a 40-minute lecture about his research during the prize ceremony which was held on June 29, 2009, at the Mathematics Institute, University of Warwick in the United Kingdom.

“This is terrific news,” said R-MC president Robert R. Lindgren. “Brian is one of Randolph-Macon’s finest and deserves this distinguished honor. We congratulate him on this exceptional achievement and are delighted that his talent is recognized throughout the world.“

Dr. Sutton’s article, “Computing the Complete CS Decomposition,” presents an algorithm that computes the cosine-sine decomposition of a partitioned unitary matrix. An algorithm is a step-by-step procedure for solving a problem, often used for calculation and data processing. The algorithm in Dr. Sutton’s research appears to be the only stable algorithm for computing the CS decomposition, which breaks a unitary matrix into a product of rotations in a high dimensional space.

In an abstract to describe the research, Sutton writes, “Although the existence of the CS decomposition (CSD) has been recognized since 1977, prior algorithms compute only a reduced version. This reduced version, which might be called a 2-by-1 CSD, is equivalent to two simultaneous singular value decompositions. The new algorithm computes the complete 2-by-2 CSD, which requires the simultaneous diagonalization of all four blocks of a unitary matrix partitioned into a 2-by-2 block structure.”

Dr. Sutton began work on the CS decomposition in the fall of 2004. His algorithm uses a tool called QR iteration, which was developed by John Francis in 1959. A mini-symposium was held June 23-26, 2009, in Glasgow, Scotland, to celebrate the 50th anniversary of his discovery. Dr. Sutton had the privilege of meeting Francis during the event.

The notable Leslie Fox Prize is awarded every other year to promising mathematicians who are under the age of 31. The submissions are judged by a committee of respected peers based on originality and quality of the subject. Special consideration is also given to the suitability of the material for a 40-minute lecture to an audience of numerical analysts. Leslie Fox was a British mathematician noted for his contributions to numerical analysis. He earned a DPhil in computational and engineering mathematics at Oxford under the supervision of Sir Richard Southwell. Dr. Fox was named the director of the University of Oxford’s Computing laboratory and later became the first professor of numerical analysis at the University. The Leslie Fox Prize was established upon his retirement in 1983 with the aim of giving encouragement and recognition to young research workers.

Dr. Sutton joined the faculty at Randolph-Macon College in 2005. He earned bachelor's degrees in both mathematics and computer science at Virginia Tech and his Ph.D. at the Massachusetts Institute of Technology. He has been an invited presenter at more than a dozen conferences and lectures. Dr. Sutton’s research and other writings have been published in several academic and instructional publications. He plans to continue exploring the CS decomposition and its applications, possibly even to quantum computing.