Akshay S. Rane

collaborators

4 papers

math.NA2026

Projection-based approximations for eigenvalue problems of Fredholm integral operators with Green's kernels

Shashank K. Shukla, Gobinda Rakshit, Akshay S. Rane

We consider the eigenvalue problem $K x = I^» x$ . Our analysis focuses on the convergence rates of eigenvalue and spectral subspace approximations for compact linear integral operato…

math.NA2024

Asymptotic expansions for approximate solutions of boundary integral equations

Akshay Rane, Kunalkumar Shelar

This paper uses the Modified Projection Method to examine the errors in solving the boundary integral equation from Laplace equation. The analysis uses weighted norms, and parallel…

math.FA2024

Joint spectrum of matrix and operator tuples on spaces over bi complex numbers

Akshay Rane

In this paper, we generalize the notion of joint eigenvalues and joint spectrum of matrices and operator tupples on a bi complex Hilbert space. We observe that unlike the spectrum…

math.NA2024

A note on improvement by iteration for the approximate solutions of second kind Fredholm integral equations with Green's kernels

Gobinda Rakshit, Shashank K. Shukla, Akshay S. Rane

Consider a linear operator equation $x - K x = f$ , where $f$ is given and $K$ is a Fredholm integral operator with a Green's function type kernel defined on $C [0, 1]$ . For $r \geq 0…