Institute for Computational and Mathematical Engineering (ICME)

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  • Sagar Vare

    Sagar Vare

    Masters Student in Computational and Mathematical Engineering, admitted Autumn 2015

    BioI love tackling puzzles and have a strong mathematical background. I enjoy engineering applications, and aim to create a positive impact in this wold. Additionally I am interested in fields which are painfully common in the silicon valley and buzz words thrown around quite "carelessly" i.e. "Deep Learning", "Machine Learning", "Internet of Things". I also am an amateur chess player, and have dabbled a little bit in blindfolded chess too(this is something that I am working on currently)! Feel free to contact me if you find any of the above interesting (especially the chess part).

  • Varun Vasudevan

    Varun Vasudevan

    Ph.D. Student in Computational and Mathematical Engineering, admitted Autumn 2016

    Current Research and Scholarly InterestsMaster's Thesis

    Title: Best rank-1 approximations without orthogonal invariance for the 1-norm.

    Abstract: Data measured in the real-world is often composed of both a true signal, such as an image or experimental response, and a perturbation, such as noise or weak secondary effects. Low-rank matrix approximation is one commonly used technique to extract the true signal from the data. Given a matrix representation of the data, this method seeks the nearest low-rank matrix where the distance is measured using a matrix norm.

    The classic Eckart-Young-Mirsky theorem tells us how to use the Singular Value Decomposition (SVD) to compute a best low-rank approximation of a matrix for any orthogonally invariant norm. This leaves as an open question how to compute a best low-rank approximation for norms that are not orthogonally invariant, like the 1-norm.

    In this thesis, we present how to calculate the best rank-1 approximations for 2-by-n and n-by-2 matrices in the 1-norm. We consider both the operator induced 1-norm (maximum column 1-norm) and the Frobenius 1-norm (sum of absolute values over the matrix). We present some thoughts on how to extend the arguments to larger matrices.