20 citations · 45 across the 20 of their papers we have counts for
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A fast solver for ill-conditioned linear systems using randomized stable solutions of its blocks
Suvendu Kar, Murugesan Venkatapathi
We present an enhanced version of the row-based randomized block-Kaczmarz method to solve a linear system of equations. This improvement makes use of a regularization during block…
An Optimal Least-Square Solver For Scaled Partial-Isometric Linear Systems
Suvendu Kar, Murugesan Venkatapathi
We present an direct least-squares solver for linear systems with a scaled partial isometry. The proposed algorithm is also useful when the system is block dia…
Efficient approximations of matrix multiplication using truncated decompositions
Suvendu Kar, Hariprasad M., Sai Gowri J. N. +1
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large de…
Approximations for modeling light scattering by spheres with uncertainty in physical parameters
Akif Khan, Murugesan Venkatapathi
Uncertainty in physical parameters can make the solution of forward or inverse light scattering problems in astrophysical, biological, and atmospheric sensing applications, cost pr…
Circulant decomposition of a matrix and the eigenvalues of Toeplitz type matrices
Hariprasad M., Murugesan Venkatapathi
We begin by showing that any matrix can be decomposed into a sum of circulant matrices with periodic relaxations on the unit circle. This decomposition is orthogon…
An O(n) algorithm for generating uniform random vectors in n-dimensional cones
Arun I., Murugesan Venkatapathi
Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On t…
An algorithm for estimating volumes and other integrals in dimensions
Arun I., Murugesan Venkatapathi
The computational cost in evaluation of the volume of a body using numerical integration grows exponentially with dimension of the space . The most generally applicable algorith…
Error estimators and their analysis for CG, Bi-CG and GMRES
Puneet Jain, Krishna Manglani, Murugesan Venkatapathi
The demands of accuracy in measurements and engineering models today, renders the condition number of problems larger. While a corresponding increase in the precision of floating p…
Semi-analytical solutions for eigenvalue problems of chains and periodic graphs
Hariprasad M., Murugesan Venkatapathi
We first show the existence and nature of convergence to a limiting set of roots for polynomials in a three-term recurrence of the form a…
Estimation of errors in iterative solutions of a non-symmetric linear system
Aashish Vishwakarma, Murugesan Venkatapathi
Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such…
Non-stationary extremal eigenvalue approximations in iterative solutions of linear systems and estimators for relative error
Divya Anand Subba, Murugesan Venkatapathi
Non-stationary approximations of the final value of a converging sequence are discussed, and we show that extremal eigenvalues can be reasonably estimated from the CG iterates with…