Abstract. This article introduces HODLR2D, a new hierarchical low-rank representation for a class of dense matrices arising out of \(N\) -body problems in two dimensions. Using this new hierarchical framework, we propose a new fast matrix-vector product that scales almost linearly. We apply this fast matrix-vector product to accelerate the iterative solution of large dense linear systems arising out of radial basis function interpolation and discretized integral equation. The space and computational complexity of HODLR2D matrix-vector products scale as \(\mathcalO(pN \log (N))\) , where \(p\)is the maximum rank of the compressed matrix subblocks. For the logarithmic kernel function, we prove that \(p ∈\mathcalO \left (\log \left (N\right ) \log \left (\log \left (N\right ) \right ) \right )\) . We also numerically observe a similar scaling for other kernel functions in 2D. We thereby demonstrate that the storage and computational complexity of HODLR2D matrix-vector products remain tractable for large \(N\) . Additionally, we also study the parallel scalability of HODLR2D as part of this article.
@article{hodlr2d,author={Kandappan, V A and Gujjula, Vaishnavi and Ambikasaran, Sivaram},title={HODLR2D: A New Class of Hierarchical Matrices},journal={SIAM Journal on Scientific Computing},volume={45},number={5},pages={A2382-A2408},year={2023},doi={10.1137/22M1491253},eprint={{https://doi.org/10.1137/22M1491253}},}
arXiv
HODLR3D: Hierarchical matrices for N-body problems in three dimensions
V A Kandappan, Vaishnavi Gujjula, and Sivaram Ambikasaran
@misc{kandappan2023hodlr3d,title={HODLR3D: Hierarchical matrices for $N$-body problems in three dimensions},author={Kandappan, V A and Gujjula, Vaishnavi and Ambikasaran, Sivaram},year={2023},eprint={2307.16303},archiveprefix={arXiv},primaryclass={math.NA}}
arXiv
HODLRdD: A new Black-box fast algorithm for N-body problems in d-dimensions with guaranteed error bounds
Ritesh Khan, V A Kandappan, and Sivaram Ambikasaran
@misc{khan2023hodlrdd,title={{HODLR$d$D: A new Black-box fast algorithm for $N$-body problems in $d$-dimensions with guaranteed error bounds}},author={Khan, Ritesh and Kandappan, V A and Ambikasaran, Sivaram},year={2023},eprint={2209.05819},archiveprefix={arXiv},primaryclass={math.NA}}
2021
SPRINGER
Machine Learning in Finance: Towards Online Prediction of Loan Defaults Using Sequential Data with LSTMs
V A Kandappan, and A. G. Rekha
In Soft Computing: Theories and Applications, 2021
In recent times, machine learning is finding many important use cases in the financial services industry. Financial datasets usually pose significant statistical challenges, and hence, traditional econometric methods fail in many practical applications. Though several approaches are suggested and being used, to predict whether a borrower would default on the loan availed, it is still an open challenge. In this work, two approaches are proposed based on LSTM (Long Short Term Memory) along with a hybrid neural network architecture to understand the context between financial transactions and loan defaults. The novelty of the proposed methods is in how they handle structured data and the associated temporal data. Further, the performance of the proposed approaches using debit card transactions and loan application information of customers to predict default is demonstrated. The experiments provided promising accuracies. Bidirectional LSTMs with a hybrid architecture achieve an accuracy of 94%. Hybrid neural network architectures used in this work provide an appropriate direction for making an early warning system through online loan default prediction.Kandappan, V. A.Rekha, A. G.
@inproceedings{mlrnn,author={Kandappan, V A and Rekha, A. G.},title={Machine Learning in Finance: Towards Online Prediction of Loan Defaults Using Sequential Data with LSTMs},booktitle={Soft Computing: Theories and Applications},year={2021},publisher={Springer Singapore},address={Singapore},pages={53--62},isbn={978-981-16-1696-9}}
2015
IJAER
Effect of time sychronization error in phasor measurement unit
Gomathi Venugopal, and V A Kandappan
International journal of applied engineering research, Dec 2015
@article{pmu,author={Venugopal, Gomathi and Kandappan, V A},year={2015},month=dec,title={Effect of time sychronization error in phasor measurement unit},volume={10},journal={International journal of applied engineering research}}
