8 papers
On a Class of Block-Regularized Preconditioned Iterative Methods for Indefinite Least-Squares Problems
Pinki Khatun
This paper proposes a novel block-regularized splitting (BRS) framework for the efficient solution of indefinite least-squares (ILS) problems. Based on a block-wise regularization…
Physics-Informed Broad Learning System: An Efficient Backpropagation-Free Framework for Solving Partial Differential Equations
Pinki Khatun, M. Sajid, Abhinav Jha +1
Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural…
On the Diophantine Equation over
Pinki Khatun
I investigate the Diophantine equation where and . Using the arithmetic of the quadratic integer r…
Sparsity-Preserving Structured Backward Error Analysis for Double Saddle Point Problems
Sk. Safique Ahmad, Pinki Khatun
Backward error (BE) analysis emerges as a powerful tool for assessing the backward stability and strong backward stability of numerical algorithms. In this paper, we explore struct…
A Class of Generalized Shift-Splitting Preconditioners for Double Saddle Point Problems
Sk. Safique Ahmad, Pinki Khatun
In this paper, we propose a generalized shift-splitting (GSS) preconditioner, along with its two relaxed variants to solve the double saddle point problem (DSPP). The convergence o…
Structured Backward Errors of Sparse Generalized Saddle Point Problems with Hermitian Block Matrices
Sk. Safique Ahmad, Pinki Khatun
In this paper, we derive the structured backward error (BE) for a class of generalized saddle point problems (GSPP) by preserving the sparsity pattern and Hermitian structures of t…