Demmel made 1975 his bachelor's degree at Caltech in 1983 and his doctorate at the University of California, Berkeley, in computer science at William Kahan (A numerical analyst 's Jordan canonical form ). From 1983 he was in the faculty of computer science at New York University and from 1990 professor at Berkeley, where he is Carl Dehmel Distinguished Professor in 2004.
He is known for his contribution to LAPACK and ScaLAPACK, software libraries for numerical linear algebra for high -performance computers. 1999 won his multigrid FEM program Prometheus (written with Mark Adams and Robert Taylor) the Carl Benz Award and the 2004 Gordon Bell price. In 1993 he received the James H. Wilkinson Prize, the Presidential Young Investigator Award, the 1986 Leslie Fox Prize of the Institute of Mathematics and its Applications and the 2010 Sidney Fernbach Award from the IEEE. He is a member of the National Academy of Engineering ( 1999) and the National Academy of Sciences ( 2011). In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing (The complexity of accurate floating point calculation ).
He is married to Katherine Yelick, who is a professor of electrical engineering and computer science at Berkeley.