Andrei Knyazev (mathematician)
Encyclopedia
Andrei Knyazev is a Russian
-American
mathematician
. He graduated from the 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. Since 1994, he is Professor of Mathematics
at the University of Colorado Denver
. His research has been supported by NSF and DOE grants since 1995.
Knyazev is mostly known for his work in numerical solution of large sparse
eigenvalue problems, particularly the iterative method LOBPCG
. An implementation of LOBPCG
is available in the public software package BLOPEX
, maintained by Knyazev. The LOBPCG has been also implemented in a popular public electronic structure calculations package ABINIT
.
Back in the Soviet Union
, Knyazev has collaborated with Bakhvalov on numerical solution of elliptic partial differential equations (PDE's) with large jumps in the main coefficients. Knyazev has also contributed to the theory of the Rayleigh–Ritz method.
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
-American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He graduated from the Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
under the supervision of Evgenii Georgievich D'yakonov
Evgenii Georgievich D'yakonov
Evgenii Georgievich D'yakonov was a Russian mathematician.D'yakonov was a Ph.D. student of Sergei Sobolev. He worked at the Moscow State University. He authored over hundred papers and several books...
in 1981 and obtained his PhD in Numerical Mathematics
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
at the Russian Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
under the supervision of Vyacheslav Ivanovich Lebedev
Vyacheslav Ivanovich Lebedev
Vyacheslav Ivanovich Lebedev was a Soviet and Russian mathematician, known for his work on numerical analysis....
in 1985. Since 1994, he is Professor of Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the University of Colorado Denver
University of Colorado Denver
The University of Colorado Denver, shortened as CU Denver, UC Denver, or UCD, is a public university in the United States state of Colorado. It is one of three schools of the University of Colorado system. The university has two campuses — one in downtown Denver at the Auraria Campus, and the other...
. His research has been supported by NSF and DOE grants since 1995.
Knyazev is mostly known for his work in numerical solution of large sparse
Sparse matrix
In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros . The term itself was coined by Harry M. Markowitz....
eigenvalue problems, particularly the iterative method LOBPCG
LOBPCG
Locally Optimal Block Preconditioned Conjugate Gradient Method is an algorithm, proposed in , for finding the largest eigenvalues and the corresponding eigenvectors of a symmetric positive definite generalized eigenvalue problem.A x= \lambda B x,for a given pair of complex Hermitian or real...
. An implementation of LOBPCG
LOBPCG
Locally Optimal Block Preconditioned Conjugate Gradient Method is an algorithm, proposed in , for finding the largest eigenvalues and the corresponding eigenvectors of a symmetric positive definite generalized eigenvalue problem.A x= \lambda B x,for a given pair of complex Hermitian or real...
is available in the public software package BLOPEX
BLOPEX
The Block Locally Optimal Preconditioned Eigenvalue Xolvers is a suite of routines for the scalable solution of eigenvalue problems. Its object-oriented design allows easy portability. Currently available built-in interfaces are Hypre, PETSc, MATLAB, GNU Octave, and a serial stand-alone version...
, maintained by Knyazev. The LOBPCG has been also implemented in a popular public electronic structure calculations package ABINIT
ABINIT
ABINIT is an open-source suite of programs for materials science, distributed under the GNU General Public License. ABINIT implements density functional theory, using a plane wave basis set and pseudopotentials, to compute the electronic density and derived properties of materials ranging from...
.
Back in the Soviet Union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
, Knyazev has collaborated with Bakhvalov on numerical solution of elliptic partial differential equations (PDE's) with large jumps in the main coefficients. Knyazev has also contributed to the theory of the Rayleigh–Ritz method.