PeopleofSuperintelligence

Researcher

Andrew Knyazev

Also known as Andrei Knyazev, Андрей Владимирович Князев

Andrew Knyazev is a mathematician whose eigenvalue work connects to machine learning through spectral clustering. He graduates from Moscow State University in 1981, defends a candidate dissertation on eigenvalue calculations in 1985, and teaches mathematics at the University of Colorado Denver from 1994 to 2014. In 2001, he describes the LOBPCG method for symmetric eigenvalue problems; with David Zhuzhunashvili, he applies it to graph Laplacians used in a 2017 spectral-clustering paper. At MERL, his research covers image and video processing, data sciences, optimal control, materials, and numerical simulation. He becomes a SIAM Fellow in 2016 and, as of October 2026, is Professor Emeritus at CU Denver.

Now at
University of Colorado Denver
Works
150
Citations
2,680
h-index
24
Badges

Publication numbers from OpenAlex, as of 18 October 2026.

Timeline

  1. 1959–1994

    From Moscow to the Courant Institute

    Born in Moscow in 1959, he graduates from Moscow State University's Faculty of Computational Mathematics and Cybernetics in 1981 and defends a candidate dissertation on eigenvalue calculations in 1985. He works at the Kurchatov Institute in 1981–1983 and the Academy of Sciences' Numerical Mathematics department through 1992, then works at New York University's Courant Institute in 1993–1994.

  2. 1994–2014

    Professor at CU Denver

    In 1994, he becomes a mathematics professor at the University of Colorado Denver and serves until retirement in 2014.

  3. 2001

    The LOBPCG method

    In a 2001 conference abstract, he describes the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method for symmetric eigenvalue problems and proposes a multigrid preconditioner.

  4. 2016

    A SIAM Fellowship

    He becomes a SIAM Fellow in 2016 for contributions to computational mathematics and numerical methods for eigenvalue problems.

  5. By 2017

    Research at MERL

    By 2017, his MERL research covers algorithms for image and video processing, data sciences, optimal control, materials, and simulation of complex phenomena, a focus that starts in 2012.

  6. 2017

    Spectral graph clustering

    With David Zhuzhunashvili, he applies LOBPCG to graph-Laplacian eigenvalue problems in a 2017 machine-learning paper on spectral clustering.

  7. 2016

    A Professor Emeritus title

    He receives the title of Professor Emeritus at the University of Colorado Denver in 2016.

  8. As of October 2026

    Professor Emeritus at CU Denver

    As of October 2026, he is Professor Emeritus in Mathematical and Statistical Sciences at the University of Colorado Denver.

Career

  1. Since 1994University of Colorado DenverMathematics Professor
  2. 2012–2019Mitsubishi Group
  3. 1993–1994Courant Institute of Mathematical Sciences
  4. 1983–1992Academy of Sciences
  5. 1981–1983Kurchatov Institute

Education

  1. 1981Lomonosov Moscow State University

From the biography and OpenAlex affiliations (the years of papers that list the organization), so some years are approximate.

Most-cited works

  1. Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method2001 · SIAM Journal on Scientific Computing · 779 citations
  2. Principal Angles between Subspaces in an A -Based Scalar Product: Algorithms and Perturbation Estimates2002 · SIAM Journal on Scientific Computing · 225 citations
  3. Large-scale ab initio calculations based on three levels of parallelization2007 · Computational Materials Science · 178 citations
  4. Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in Hypre and PETSc2007 · SIAM Journal on Scientific Computing · 109 citations
  5. Preconditioned Eigensolvers - an Oxymoron?1998 · 98 citations

From OpenAlex, as of 18 October 2026.

  1. Google has the highest combined h-index among AI organizationsIncludes New York University. Our estimates of combined and median h-index at AI organizations, using current affiliations and OpenAlex records.
  2. Stanford University trained or employed 27 of the 111 AI major-prize winners, more than any other universityIncludes New York University. Stanford University trained or employed 27 of the 111 AI major-prize winners, more than any other university. We compare doctorate and employment links for major-prize and best-paper winners.
  3. The company share of AI researchers’ top papers rose from 3% to 32%Includes Mitsubishi Group. We estimate where leading AI researchers worked when their most-cited papers appeared. The company share rose from 3% in 1975–1979 to 32% in 2020–2024.
  4. More people shaping AI studied at Massachusetts Institute of Technology than at any other institutionIncludes New York University. Our estimates of where the people shaping AI studied and where their careers led, from education records in cited biographies.

Colleagues

People with dated positions at the same organization in the same years.

Sources and credits

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  1. Князев, Андрей Владимирович ru.wikipedia.org. Checked 18 October 2026.
  2. CM conference abstract: Andrew Knyazev. Copper Mountain 2001 grandmaster.colorado.edu. Checked 18 October 2026.
  3. Fellow of the Society for Industrial and Applied Mathematics (SIAM) merl.com. Checked 18 October 2026.
  4. Society for Industrial and Applied Mathematics panel for students on careers in industry merl.com. Checked 18 October 2026.
  5. Preconditioned Spectral Clustering for Stochastic Block Partition Streaming Graph Challenge arxiv.org. Checked 18 October 2026.
  6. Professor Emeritus University of Colorado Denver merl.com. Checked 18 October 2026.
  7. Andrew Knyazev | Mathematical and Statistical Sciences | CU Denver College of Liberal Arts and Sciences clas.ucdenver.edu. Checked 18 October 2026.