## Obituaries: Ralph E. Kleinman

**April 14, 1998**

Ralph E. Kleinman, 1929–1998

Ralph Kleinman was born in 1929 and grew up in Lindenhurst and Forest Hills, New York. He received a BA in mathematics from New York University in 1950 and an MA in mathematics from the University of Michigan in 1951. He worked at Michigan's Radiation Laboratory for two years before serving in the U.S. Army at Redstone Arsenal in Alabama. He returned to the Radiation Lab in 1955; while there, he received a Fulbright fellowship to study at the Delft University of Technology, where he obtained a Doctor in de Technische Wetenschappen (equivalent to a U.S. PhD) in 1961.

Until 1968, when he moved to Delaware, Kleinman was a research mathematician at the Radiation Lab of the University of Michigan. In his early work he concentrated on radiation and scattering, providing rigorous foundations for computational work being carried out at the lab. He was attracted to low-frequency scattering early in his career and returned to the subject often. At the time of his death, he had just completed a volume on low-frequency scattering with George Dassios of the University of Patras.

Kleinman was known for his work on integral equations applied to problems in scattering and wave propagation, in which he addressed theoretical issues that are relevant to computation. Later in his career, he branched out in several new directions, among them inverse problems and optimization problems associated with radiation and scattering. His many co-authors in these areas include Tom Angell of the University of Delaware and Gary Roach of the University of Strathclyde. In the mid-1980s, electrical engineers were beginning to use iterative methods in the solution of scattering problems. The basic method came in many different flavors. Among Kleinman's accomplishments was to gather all these different methods within one mathematical framework, and to explain their convergence properties.

Most notable among his contributions to inverse scattering problems was his work with Peter van den Berg of the Delft University of Technology, in which they proposed a reconstruction procedure called the modified gradient technique. This method is computationally very efficient and has been tested on electromagnetic scattering data collected by the Air Force Rome Laboratory in Ipswich, Massachusetts. Indeed, one of Kleinman's remarkable achievements in this field was to organize several competing groups in inverse scattering, convincing them to apply their methods to real data and report their findings.

Most recently, he collaborated with George Hsiao of the University of Delaware on a procedure for using the result of a computation to estimate the error in the solution of an integral equation arising in a scattering problem. An approach of this type is particularly valuable because of the confidence it can give the user in the output of a calculation.

Perhaps what made Kleinman's contributions to scattering and wave propagation unique was his ability to recognize the real problems facing the engineers who solve these problems in the real world, and to provide useful answers to them through the application of mathematical analysis. It was for such insight and ability that he was named a Fellow of IEEE in 1994.

Over the years, Ralph collaborated with many colleagues in the U.S. and Europe. He was an ideal person to work with: easy-going, energetic, full of ideas, and willing to do the hard work that came with the joint project. Many of these collaborations blossomed into lifelong friendships.

In the classroom, Ralph was an inspiring and enthusiastic teacher. He was adviser to nine PhD students in the course of his career and served on dissertation committees of numerous others in the U.S. and Europe. One of his achievements at Delaware was his role in establishing the American Association of University Professors (AAUP) as the bargaining unit representing the faculty at the university. He was active in the faculty government at Delaware, serving as president of both the Faculty Senate and the College of Arts and Science Senate. He also served as president of the Delaware chapter of AAUP.

Ralph was responsible for organizing several conferences and workshops. In 1993 he was the organizer of the SIAM-INRIA Conference on Mathematical and Numerical Aspects of Wave Propagation, held in Newark, Delaware.

An inspiring teacher, a respected colleague, and a wonderful friend, Ralph will be missed by all who knew him.

---*Fadil Santosa*, University of Minnesota.