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First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also determine minimal structured perturbations for which approximate eigenelements are exact eigenelements of the perturbed… (More)

- Bibhas Adhikari, Rafikul Alam
- SIAM J. Matrix Analysis Applications
- 2009

Structured backward perturbation analysis plays an important role in the accuracy assessment of computed eigenelements of structured eigenvalue problems. We undertake a detailed structured backward perturbation analysis of approximate eigenelements of linearly structured matrix pencils. The structures we consider include, for example, symmetric,… (More)

- Bibhas Adhikari
- 2009

We derive computable expressions of structured backward errors of approximate eigenelements of ∗-palindromic and ∗-anti-palindromic matrix polynomials. We also characterize minimal structured perturbations such that approximate eigenelements are exact eigenelements of the perturbed polynomials. We detect structure preserving linearizations which have almost… (More)

This work is concerned with eigenvalue problems for structured matrix polynomials, including complex symmetric, Hermitian, even, odd, palindromic, and anti-palindromic matrix polynomials. Most numerical approaches to solving such eigenvalue problems proceed by linearizing the matrix polynomial into a matrix pencil of larger size. Recently, linearizations… (More)

- Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee
- Quantum Information Processing
- 2016

Building upon our previous work, on graphical representation of a quantum state by signless Laplacian matrix, we pose the following question. If a local unitary operation is applied to a quantum state, represented by a signless Laplacian matrix, what would be the corresponding graph and how does one implement local unitary transformations graphically? We… (More)

- Bibhas Adhikari, Subhashish Banerjee, Satyabrata Adhikari, Atul Kumar
- Quantum Information Processing
- 2017

- Rohan Sharma, Bibhas Adhikari, Abhishek Mishra
- CALDAM
- 2015

Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two graphs, we define corona graphs. Given a small simple connected graph which we call basic graph, corona graphs are defined… (More)

- Rohan Sharma, Bibhas Adhikari, Abhishek Mishra
- Discrete Applied Mathematics
- 2017

- Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee
- ArXiv
- 2017

In this paper we determine the class of quantum states whose density matrix representation can be derived from graph Laplacian matrices associated with a weighted directed graph and we call them graph Laplacian quantum states. Then we obtain structural properties of these graphs such that the corresponding graph Laplacian states have zero quantum discord by… (More)

- Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee
- Quantum Information Processing
- 2017

Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are reflected in the structure of the corresponding graph. Here, we attempt to develop a graph theoretic study of quantum discord… (More)