Person: Sahu, Nabin Kumar
Loading...
Name
Nabin Kumar Sahu
Job Title
Faculty
Email Address
Telephone
079-68261642
Birth Date
Specialization
Frame Theory, Optimization Theory and Applications, Variational Inequalities
Abstract
Biography
As a person from Pure Mathematics group, I work in the Theory of Optimization and the Theory of Frames. The theory of frames is largely applied in Signal Processing and Image processing. Optimization also plays a significant role in Machine learning and Data analysis. So although I belong to Pure Mathematics group, I extend my research area towards applications.
As a person from Pure Mathematics group, I work in the Theory of Optimization and the Theory of Frames. The theory of frames is largely applied in Signal Processing and Image processing. Optimization also plays a significant role in Machine learning and Data analysis. So although I belong to Pure Mathematics group, I extend my research area towards applications.
As a person from Pure Mathematics group, I work in the Theory of Optimization and the Theory of Frames. The theory of frames is largely applied in Signal Processing and Image processing. Optimization also plays a significant role in Machine learning and Data analysis. So although I belong to Pure Mathematics group, I extend my research area towards applications.
Research Projects
Organizational Units
Name
13 results
Search Results
Now showing 1 - 10 of 13
Publication Metadata only Implicit variational inclusions and algorithms involving (A, ?)-monotone operators in 2-uniformly smooth Banach spaces(David Publishing, 01-06-2015) Sahu, Nabin Kumar; DA-IICT, GandhinagarPublication Metadata only Basis extension and construction of tight frames(Raimag Press, 01-10-2023) Sahu, Nabin KumarThe notion of compression has received enormous attention in recent years because of its necessity in terms of the computational cost and other applicable features. But many times the notion expansion appears to be quite useful. Tight frames are quite useful in signal reconstruction, signal and image de-noising, compressed sensing because of the availability of a simple, explicit reconstruction formula. So in this paper, we discuss the extension of a basis by including some very sparse (at most two nonzero components) vectors so that the new frame becomes a tight frame. We do the basis extension in finite dimensional Hilbert spaces (both real and complex) to construct tight frames. We formulate constructive algorithms to do the aforementioned task. The algorithms guarantee us to produce tight frames with very less computational cost, and the new tight frames compensate for multiple era-sures. The algorithms also do not disturb the vectors in the given basis. We also present one application of the aforementioned concept.Publication Metadata only Representation of frames as regular k-distance sets(Springer, 13-10-2022) Rajput, Ekta; Sahu, Nabin Kumar; DA-IICT, Gandhinagar; Rajput, Ekta (201621011)Frames can be viewed as more flexible substitutes of bases in Hilbert spaces. In this paper, we introduce the concept of regular k-distance frame in Hilbert space. Here, we discuss various characteristics of regular k-distance sets as well as focus on k-distance tight frames for the underlying space. We also discuss the dual frames for regular k-distance sets and provide some examples. At the end we establish a perturbation result for regular k-distance frames.Publication Metadata only Approximation solvability of a class of A-monotone implicit variational inclusion problems in semi-inner product spaces(Elsevier, 01-06-2014) Sahu, Nabin Kumar; Mohapatra, Ram N; Nahak, C; Nanda, S; DA-IICT, GandhinagarThis paper deals with the existence of solutions for a class of nonlinear implicit variational inclusion problems in semi-inner product spaces. We construct an iterative algorithm for approximating the solution for the class of implicit variational inclusions problems involving�A-monotone and�H-monotone operators by using the generalized resolvent operator technique.Publication Metadata only A New Class of Generalized Monotone Mappings and Variational inclusion Problems in Banach Spaces(01-01-2016) Sahu, Nabin Kumar; Mohapatra, Ram; Nahak, C; Mahato, N K; DA-IICT, GandhinagarIn this paper, we introduce and study a new class of variational inclusions in Banach spaces. For solving such class of variational inclusions, we introduce a new notion of B-monotone operator and prove the Lipschitz continuity of the proximal mapping associated with the B-monotone operator. By using the proximal mapping, an iterative algorithm for solving such class of variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of iterative sequence generated by the algorithm.Publication Metadata only System of nonlinear variational inclusion problems with (A, ?-maximal monotonicity in Banach spaces(IAPress, 01-09-2017) Sahu, Nabin Kumar; Mahato, N K; Mohapatra, Ram N; Sahu, Nabin Kumar; Sahu, Nabin Kumar; Sahu, Nabin Kumar; Sahu, Nabin Kumar; Sahu, Nabin Kumar; DA-IICT, GandhinagarThis paper deals with a new system of nonlinear variational inclusion problems involving $(A,\eta)$-maximal relaxed monotone and relative $(A,\eta)$-maximal monotone mappings in 2-uniformly smooth Banach spaces. Using the generalized resolvent operator technique, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also proved for other system of variational inclusion problems involving relative $(A,\eta)$-maximal monotone mappings and $(H,\eta)$-maximal monotone mappings.Publication Metadata only Existence results for trifunction equilibrium problems and fixed point problems(Springer, 01-03-2019) Mahato, Nihar Kumar; Noor, Muhammad Aslam; Sahu, Nabin Kumar; DA-IICT, GandhinagarIn this paper, we establish the existence and uniqueness solutions of trifunction equilibrium problems using the generalized relaxed�-monotonicity in Banach spaces. By using the generalized�f-projection operator, a hybrid iteration scheme is presented to find a common element of the solutions of a system of trifunction equilibrium problems and the set of fixed points of an infinite family of quasi--nonexpansive mappings. Moreover, the strong convergence of our new proposed iterative method under generalized relaxed�-monotonicity is considered.Publication Metadata only Woven g-frames in Hilbert C*-modules(PKP, 30-03-2021) Rajput, Ekta; Sahu, Nabin Kumar; Mishra, Vishnu Narayan; DA-IICT, Gandhinagar; Rajput, Ekta (201621011)Woven frames are motivated from distributed signal processing with potential applications in wireless sensor networks. g-frames provide more choices on analyzing functions from the frame expansion coefficients. The objective of this paper is to introduce woven g-frames in Hilbert C*-modules, and to develop its fundamental properties. In this investigation, we establish sufficient conditions under which two g-frames possess the weaving properties. We also investigate the sufficient conditions under which a family of g-frames possess weaving properties.Publication Metadata only Controlled g-frames in Hilbert C*-modules(ResearchGate, 05-09-2021) Sahu, Nabin Kumar; DA-IICT, GandhinagarThe controlled frame was introduced by Balazs et al. [2], with the aim to improve the efficiency of the iterative algorithms constructed for inverting the frame operator. In this paper, the concept of controlled g-frames is introduced in Hilbert C*-modules. The equivalent condition for controlled g-frame is established using the operator theoretic approach. Some characterizations of controlled g-frames and controlled g-Bessel sequences are found out. Moreover, the relationship between g-frames and controlled g-frames are established. At the end, some perturbation results on controlled g-frames are proved.Publication Metadata only A Comparative Study of Various Artificial Intelligence Based Agents for the Game of Angry Birds with and without Splitting(Iopscience) Kumar, Ankit; Jani, Kunal; Sahu, Nabin Kumar; DA-IICT, Gandhinagar; Kumar, Ankit (201701001); Jani, Kunal (201601444)In a game of angry birds, birds are fired from a slingshot and are targeted towards stationary pigs located at different fixed distances from the slingshot. The angry birds have to be fired in such a way that it lands as close as possible to the pigs� location. The goal is to develop an artificial intelligence-based model that would play the angry birds game based on the past human experience. In this game, the user will give the initial velocity and the angle of projection. Based on these parameters, the shot will be played, and the outcome is stored as a tuple consisting of the initial velocity, the angle of projection, and the location of pigs that have not been destroyed in a database. The machine learning-based agent reads the data from the database, trains itself based on the outcome of previous shots stored in the database, and plays the best possible shot according to the data retrieved from the database. Two machine learning models have been proposed, which are the K Nearest Neighbours model and the Naive Bayes model. The third model is the stochastic gradient descent model, which plays a shot based on the minimization of the distance between the angry bird and the pig using an objective function in terms of the initial velocity and splitting angle. The performance of both these agents has been compared with the human agent�s performance in terms of the average number of wins per 100 games.