**Andrei (Andrew) Knyazev** (Russian: Андрей Владимирович Князев) 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 (Russian: Евгений Георгиевич Дьяконов) in 1981 and obtained his PhD in Numerical Mathematics at the Russian Academy of Sciences under the supervision of Vyacheslav Ivanovich Lebedev (Russian: Вячеслав Иванович Лебедев) in 1985. He worked at the Kurchatov Institute in 1981-1983, and then to 1992 at the Institute of Numerical Mathematics (Russian: ru:Институт вычислительной математики РАН) of the Russian Academy of Sciences, headed by Gury Marchuk (Russian: Гурий Иванович Марчук).

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 in 2016.

In 2012, Knyazev took a research position at the Mitsubishi Electric Research Laboratories (MERL). 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 patents and publications.

Knyazev was mostly known for his work in numerical solution of large sparse eigenvalue problems, particularly preconditioning and the iterative method LOBPCG. An implementation of LOBPCG was available in the public software package BLOPEX. A popular public electronic structure calculations package ABINIT used LOBPCG 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 (Russian: Николай Серге́евич Бахвалов) on numerical solution of elliptic partial differential equations (PDE's) with large jumps in the main coefficients. Jointly with his Ph.D. students, Knyazev pioneered using majorization for bounds in the Rayleigh–Ritz method (see and references there) and contributed to the theory of angles between flats.