शिवराम् अम्बिकासरन् (Sivaram Ambikasaran)

Assistant Professor / Courant Instructor
firstname (at) cims (dot) nyu (dot) edu
Department of Mathematics
Courant Institute of Mathematical Sciences
New York University
Warren Weaver Hall, Room-1105A,
251, Mercer Street,
New York, NY 10012


  • Ph.D. in Computational & Mathematical Engineering, Stanford, 2013

  • M.S. in Computational & Mathematical Engineering, Stanford, 2013

  • M.S. in Statistics, Stanford, 2012

  • B.Tech. & M.Tech. in Aerospace Engineering, Indian Institute of Technology Madras, 2007

  • Publications

    (14) Sivaram Ambikasaran, Carlos Borges, Lise-Marie Imbert-Gerard, Leslie Greengard, "Fast, adaptive, high order discretization of the Lippmann-Schwinger equation in two dimension", in review Preprint*

    (13) Sivaram Ambikasaran, "Generalized Rybicki Press algorithm", Numerical Linear Algebra with Applications. Preprint*

    (12) Sivaram Ambikasaran, Eric Darve, "The Inverse Fast Multipole Method" Preprint*

    (11) Sivaram Ambikasaran, Michael O'Neil, "Fast symmetric factorization of hierarchical matrices with applications", in review Preprint*

    (10) Jun Lai, Sivaram Ambikasaran, Leslie F. Greengard, "A fast direct solver for high frequency scattering from a large cavity in two dimensions", SIAM Journal of Scientific Computing. Preprint*
    Here is a video of scattering from an engine shaped cavity. Fast direct solver is especially attractive in the present context, since it permits the computation of the scattered field for multiple incident angles in a negligible amount of time.

    (9) Sivaram Ambikasaran, Daniel Foreman-Mackey, Leslie Greengard, David W. Hogg, Michael O'Neil, "Fast Direct Methods for Gaussian Processes and the Analysis of NASA Kepler Mission Data", Transactions on Pattern Analysis and Machine Intelligence. Preprint*

    (8) Amirhossein Aminfar, Sivaram Ambikasaran, Eric Darve, "A fast block low-rank dense solver with applications to finite-element matrices", in review. Preprint*

    (7) Judith Y Li, Sivaram Ambikasaran, Eric Darve, Peter K Kitanidis, "A Kalman filter powered by \(\mathcal{H}^2\)-matrices for quasi-continuous data assimilation problems", Water Resources Research. Preprint*

    (6) Sivaram Ambikasaran, "Fast Algorithms for Dense Numerical Linear Algebra and Applications, Stanford Thesis" Official version

    (5) Sivaram Ambikasaran, Arvind Krishna Saibaba, Eric Darve, Peter K Kitanidis, "Fast Algorithms for Bayesian Inversion" Preprint*/ Book chapter

    (4) Arvind Krishna Saibaba, Sivaram Ambikasaran, Judith Y Li, Peter K Kitanidis, Eric Darve, "Application of hierarchical matrices in geostatistics", Oil & Gas Science and Technology - Revue d'IFP Energies Nouvelles. Preprint*/ Journal version

    (3) Sivaram Ambikasaran, Judith Y Li, Peter K Kitanidis, Eric Darve, "Large-scale stochastic linear inversion using hierarchical matrices", Computational Geosciences. Preprint*/ Journal version

    (2) Sivaram Ambikasaran, and Eric Darve, "An \( \mathcal{O}(N \log N) \) fast direct solver for partially hierarchical semi-separable matrices", Journal of Scientific Computing. Preprint*/ Journal version

    (1) K. Bhaskar and Sivaram Ambikasaran, "Untruncated infinite series superposition method for accurate flexural analysis of isotropic/orthotropic rectangular plates with arbitrary edge conditions", Composite Structures. Author copy*/ Journal version

    *-Preprints/Author copy are provided for timely dissemination of scholarly and technical work. Also, be aware that the journal version might be little different from the preprint in some cases.

    My codes

    All codes are made available in the hope that they will be useful, but without any warranty. All the codes can be redistributed and/or modified under the terms of MPL2 license.
    - Black Box Fast Multipole Method in two dimensions. Available at: https://github.com/sivaramambikasaran/BBFMM2D
    - Fast Linear Inversion PACKage. Available at: https://github.com/sivaramambikasaran/FLIPACK
    - Fast Direct Solver for hierarchical off-diagonal low-rank matrices. Available at: https://github.com/sivaramambikasaran/HODLR
    - Extended Semi-Separable algorithm and the generalized Rybicki Press algorithm. Available at: https://github.com/sivaramambikasaran/ESS


    Spring 2015: Discrete Mathematics
    Fall 2014: Analysis
    Spring 2014: Mathematics for Economics II
    Fall 2013: Algebra and Calculus

    Other stuff

    Other links

    Alma mater