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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Posts
Future Blog Post
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Blog Post number 4
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Blog Post number 3
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Blog Post number 2
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Blog Post number 1
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academic
publications
HODLRdD: A new black-box fast algorithm for N-body problems in d-dimensions with guaranteed error bounds: Applications to integral equations and support vector machines
Published in Journal of Computational Physics, Volume 501, 2024
We study rank of sub-matrices arising out of kernel functions. Such kernel functions are frequently encountered in a wide range of areas. To our knowledge, this is the first work to formally study rank growth of matrices arising out of a wide range of kernel functions in any dimension. In this article, we prove two new theorems bounding rank of different sub-matrices arising from these kernel functions. Bounds like these are often useful for analyzing the complexity of various hierarchical matrix algorithms. Another significant contribution of this article is that using the obtained rank bounds, we also propose a way to extend the notion of weak-admissibility for hierarchical matrices in higher dimensions. Based on this proposed weak-admissibility condition, we develop a black-box (kernel-independent) fast algorithm for N-body problems, hierarchically off-diagonal low-rank matrix in d dimensions (HODLRdD), which can perform matrix-vector products with quasi-linear complexity in any dimension d.
New Algebraic Fast Algorithms for N-body Problems in Two and Three Dimensions
Published in Communications in Computational Physics (in press), 2024
We present two new algebraic multilevel nested hierarchical matrix algorithms to perform fast matrix-vector product (MVP) for N-body problems in d dimensions. The hierarchical representations are based on our recently introduced weak admissibility condition in higher dimensions, where the admissible clusters are the far-field and the vertex-sharing clusters. Due to the use of nested form of the bases, the proposed hierarchical matrix algorithms are more efficient than the non-nested algorithms. We rely on purely algebraic low-rank approximation techniques (e.g., ACA and NCA) and develop both algorithms in a black-box (kernel-independent) fashion.
talks
Talk 1 on Relevant Topic in Your Field
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Conference Proceeding talk 3 on Relevant Topic in Your Field
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This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Teaching experience 2
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.