Andrei Knyazev (mathematician)


Andrei Knyazev is a Russian-American mathematician. He graduated from the Faculty of Computational Mathematics and Cybernetics of Moscow State University under the supervision of Evgenii Georgievich D'yakonov in 1981 and obtained his PhD in Numerical Mathematics at the Russian Academy of Sciences under the supervision of Vyacheslav Ivanovich Lebedev in 1985. He worked at the Kurchatov Institute in 1981–1983, and then to 1992 at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, headed by Gury Marchuk.
In 1993–1994, Knyazev held a visiting position at the Courant Institute of Mathematical Sciences of New York University, collaborating with Olof B. Widlund. From 1994 until retirement in 2014, he was a Professor of Mathematics at the University of Colorado Denver, supported by the National Science Foundation and United States Department of Energy grants. He was a recipient of the 2008 Excellence in Research Award, the 2000 college Teaching Excellence Award, and a finalist of the CU President's Faculty Excellence Award for Advancing Teaching and Learning through Technology in 1999.
He was awarded the title of Professor Emeritus at the University of Colorado Denver
and named the SIAM Fellow Class of 2016
and
AMS Fellow Class of 2019.
In 2012–2018, Knyazev held a Distinguished Research Scientist position at the Mitsubishi Electric Research Laboratories. His research at MERL was on algorithms for image and video processing, data sciences, optimal control, material sciences, and numerical simulation of complex phenomena, resulting in publications and 13 patent applications.
Knyazev was mostly known for his work in numerical solution of large sparse eigenvalue problems, particularly preconditioning and the iterative method LOBPCG. Knyazev's reference implementation of LOBPCG was available in the public software package BLOPEX and, e.g., the electronic structure calculations library ABINIT for wavefunction parallel optimization.
Knyazev collaborated with John Osborn
on the theory of the Ritz method in the finite element method context
and with Nikolai Sergeevich Bakhvalov on numerical solution of elliptic partial differential equations with large jumps in the main coefficients.
Jointly with his Ph.D. students, Knyazev pioneered using majorization for bounds in the Rayleigh–Ritz method
and contributed to the theory of angles between flats.