मन्त्र - "A good computation is one that does the least computation".
My research lies in the field of computational and applied mathematics mainly in fast algorithms, approximation theory and numerical linear algebra. The overarching goal of my research is to design innovative, efficient, fast, scalable algorithms taking advantage of the underlying structure such as invariance, sparsity, self-similarity, etc., for mathematical problems arising out of physical applications. To be specific, I work on fast low-rank factorizations, fast multipole method and direct solvers for hierarchical matrices with application to inverse problems, filtering, scattering, etc.

Sivaram Ambikasaran

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


  • 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 Aeropsace Engineering, Indian Institute of Technology Madras, 2007

Journal publications

  • Sivaram Ambikasaran, Eric Darve, "The Inverse Fast Multipole Method" Preprint*

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

  • Jun Lai, Sivaram Ambikasaran, Leslie F. Greengard, "A fast direct solver for high frequency scattering from a large cavity in two dimensions", accepted in SIAM Journal of Scientific Computing Preprint*

  • 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", in review Preprint*

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

  • 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*

  • Sivaram Ambikasaran, "Fast Algorithms for Dense Numerical Linear Algebra and Applications, Stanford Thesis" Author copy*/ Official version

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

  • 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

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

  • 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

  • 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, Vol. 83, No. 1, pp. 8392. 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:
- Fast Linear Inversion PACKage. Available at:
- Fast Direct Solver for hierarchical off-diagonal low-rank matrices. Available at:


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

Others stuff

Here are some of my notes
Other links

Alma mater