5 citations · 11 across the 45 of their papers we have counts for
27 papers · 1 filter
Linear stability analysis of the Lloyd algorithm on a circle
Silpi Saha, Sangita Jha, Mrinal Kanti Roychowdhury
Lloyd algorithm is the standard iterative method for computing quantizers and codebooks in source coding and vector quantization. In this article, we study the dynamical and stabil…
Quantization for a condensation system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , represents the rate at which the th quantization error of order …
Quantization dimension for a generalized inhomogeneous bi-Lipschitz iterated function system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , of a Borel probability measure on represents the sp…
Constrained quantization for the Cantor distribution with a family of constraints
Megha Pandey, Mrinal Kanti Roychowdhury
In this paper, for a given family of constraints and the classical Cantor distribution we determine the constrained optimal sets of -points, th constrained quantization error…
Constrained quantization for the Cantor distribution
Megha Pandey, Mrinal K. Roychowdhury
The theory of constrained quantization has been recently introduced by Pandey and Roychowdhury. In this paper, they have further generalized their previous definition of constraine…
Quantization dimensions for the bi-Lipschitz recurrent Iterated function systems
Amit Priyadarshi, Mrinal K. Roychowdhury, Manuj Verma
In this paper, the quantization dimensions of the Borel probability measures supported on the limit sets of the bi-Lipschitz recurrent iterated function systems under the strong op…
Quantization dimension for self-similar measures of overlapping construction
Mrinal Kanti Roychowdhury, Karoly Simon
Quantization dimension has been computed for many invariant measures of dynamically defined fractals having well separated cylinders, that is, in the cases when the so-called Open…
Quantization dimension and stability for infinite self-similar measures with respect to geometric mean error
Mrinal K. Roychowdhury, Saurabh Verma
Let be a Borel probability measure associated with an iterated function system consisting of a countably infinite number of contracting similarities and an infinite probability…
Quantization coefficients for uniform distributions on the boundaries of regular polygons
Joel Hansen, Itzamar Marquez, Mrinal K. Roychowdhury +1
In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular -sided polygons insc…
A study on Quantization Dimension in complete metric spaces
Mrinal K. Roychowdhury, S. Verma
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of fini…
Local dimensions and quantization dimensions in dynamical systems
Mrinal Kanti Roychowdhury, Bilel Selmi
Let be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of . We study the Hausdorff an…
Optimal quantization for some triadic uniform Cantor distributions with exact bounds
Mrinal Kanti Roychowdhury
Let be a set of three contractive similarity mappings such that for all , and , where $0<r<…
Quantization dimension for infinite conformal iterated function systems
Jason Atnip, Mrinal Kanti Roychowdhury, Mariusz Urbański
The quantization dimension function for an -conformal measure generated by an infinite conformal iterated function system satisfying the strong open set condition and by a…
The quantization of the standard triadic Cantor distribution
Mrinal Kanti Roychowdhury
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitel…
Optimal Quantization via Dynamics
Joseph Rosenblatt, Mrinal Kanti Roychowdhury
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We con…
Canonical sequences of optimal quantization for condensation measures
Dogan Comez, Mrinal Kanti Roychowdhury
We consider condensation measures of the form associated with the system $(\mathcal{S}, (\frac 13, \frac 13, \fr…
Asymptotics of the quantization errors for condensation measures
Mrinal Kanti Roychowdhury
Let , where , for all , and be a Borel probabi…
Least upper bound of the exact formula for optimal quantization of some uniform Cantor distributions
Mrinal Kanti Roychowdhury
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitel…
Quantization for uniform distributions on stretched Sierpiński triangles
Dogan Comez, Mrinal Kanti Roychowdhury
In this paper, we have considered a uniform probability distribution supported by a stretched Sierpiński triangle. For this probability measure, the optimal sets of -means and t…
Quantization for infinite affine transformations
Dogan Comez, Mrinal Kanti Roychowdhury
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a…
Quantization for a probability distribution generated by an infinite iterated function system
Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury
Quantization for probability distributions concerns the best approximation of a -dimensional probability distribution by a discrete probability with a given number of su…
Optimal quantization for the Cantor distribution generated by infinite similutudes
Mrinal Kanti Roychowdhury
Let be a Borel probability measure on generated by an infinite system of similarity mappings such that $P=\sum_{j=1}^\infty \frac 1{2^j}…
Quantization for uniform distributions of Cantor dusts on
Dogan Comez, Mrinal Kanti Roychowdhury
Let be a Borel probability measure on supported by the Cantor dusts generated by a set of , contractive similarity mappings satisfying the strong s…
Quantization and centroidal Voronoi tessellations for probability measures on dyadic Cantor sets
Mrinal Kanti Roychowdhury
Quantization of a probability distribution is the process of estimating a given probability by a discrete probability that assumes only a finite number of levels in its support. Ce…