Each person’s unique traits hold valuable insights into their consumer behavior, allowing scholar... more Each person’s unique traits hold valuable insights into their consumer behavior, allowing scholars and industry experts to develop innovative marketing strategies, personalized solutions, and enhanced user experiences. This study presents a conceptual framework that explores the connection between fundamental personality dimensions and users’ online shopping styles. By employing the TIPI test, a reliable and validated alternative to the Five-Factor model, individual consumer profiles are established. The results reveal a significant relationship between key personality traits and specific online shopping functionalities. To accurately forecast customers’ needs, expectations, and preferences on the Internet, we propose the implementation of two Machine Learning models, namely Decision Trees and Random Forest. According to the applied evaluation metrics, both models demonstrate fine predictions of consumer behavior based on their personality.
Advanced Computing in Industrial Mathematics, 2018
The solution, obtained in the environment of finite precision machine arithmetic must be allays a... more The solution, obtained in the environment of finite precision machine arithmetic must be allays accompanied by an analysis of the conditioning of the problem solved. The perturbation analysis derives measures for the sensitivity of the solution to perturbations in the matrix coefficients. Motivated by these, in order to ascertain the accuracy of an iteratively calculated solution to a nonlinear matrix equation arising in Tree-like stochastic processes, in this paper norm-wise, mixed and component-wise condition numbers, as well as local perturbation bounds are formulated and norm-wise non-local residual bounds are derived using the methods of nonlinear perturbation analysis (Frechet derivatives, Lyapunov majorants, fixed-point principles). The residual bounds are formulated in terms of the computed approximate solution to the equation and can be used as a stop criteria of the iterations, when solving the considered nonlinear matrix equation by a numerically stable iterative algorithm.
In this paper a local perturbation analysis of the stochastic matrix Riccati equation /SMRE/ with... more In this paper a local perturbation analysis of the stochastic matrix Riccati equation /SMRE/ with applications in linear quadratic optimization of stochastic finance models is made. Rewriting the SMRE in equivalent form of affine linear operators and applying the techniques of Frechet derivatives, absolute and relative norm-wise condition numbers are derived and local (first order) perturbation bounds for the error in the computed solution are formulated. The condition numbers and the perturbation bounds allow to estimate the conditioning of the SMRE and the accuracy of its computed by a numerical stable algorithm solution.
The paper deals with the existing methods for estimating the sensitivity of the solution to the n... more The paper deals with the existing methods for estimating the sensitivity of the solution to the nonlinear matrix equation Q
Nonsymmetric differential matrix Riccati equations arise in many problems related to science and ... more Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approaches of nonlocal perturbation analysis of the symmetric differential Riccati equation are extended to the nonsymmetric case. Applying the techniques of Fréchet derivatives, Lyapunov majorants and fixed-point principle, two perturbation bounds are derived: the first one is based on the integral form of the solution and the second one considers the equivalent solution to the initial value problem of the associated differential system. The first bound is derived for the nonsymmetric differential Riccati equation in its general form. The perturbation bound based on the sensitivity analysis of the associated linear differential system is formulated for the low-dimensional approximate solution to the large-scale nonsymmetric differential Riccati...
In this paper the problem of optimal pole assignment of linear time{invariant multi{input systems... more In this paper the problem of optimal pole assignment of linear time{invariant multi{input systems is considered. A direct parametrization of the solution for low{dimensional system is presented.
The paper deals with the perturbation estimates proposed by S. Xu [Linear Algebra Appl. 336, No. ... more The paper deals with the perturbation estimates proposed by S. Xu [Linear Algebra Appl. 336, No. 1–3, 61–70 (2001; Zbl 0992.15013)], J.-G. Sun and S. Xu [ibid. 362, 211–228 (2003; Zbl 1020.15012)] and M. M. Konstantinov et al. [in: Proceedings of the jubilee scientific conference of the University of Architecture, Civil Engineering and Geodesy on the occasion of the 60th anniversary of its foundation, Sofia, Bulgaria, November 2002. Vol. 8: Geodesy, transportation engineering, geotechnics, mathematics, physics. Sofia: University of Architecture, Civil Engineering and Geodesy. 495–504 (2002; Zbl 1187.15020)] for evaluating the sensitivity of the solution to the complex fractional-affine matrix equation X=A 1 +A 2 H X -1 A 2 relative to rounding and parameter errors. The effectiveness and reliability of the different methods are analyzed by experiments with numerical examples.
Each person’s unique traits hold valuable insights into their consumer behavior, allowing scholar... more Each person’s unique traits hold valuable insights into their consumer behavior, allowing scholars and industry experts to develop innovative marketing strategies, personalized solutions, and enhanced user experiences. This study presents a conceptual framework that explores the connection between fundamental personality dimensions and users’ online shopping styles. By employing the TIPI test, a reliable and validated alternative to the Five-Factor model, individual consumer profiles are established. The results reveal a significant relationship between key personality traits and specific online shopping functionalities. To accurately forecast customers’ needs, expectations, and preferences on the Internet, we propose the implementation of two Machine Learning models, namely Decision Trees and Random Forest. According to the applied evaluation metrics, both models demonstrate fine predictions of consumer behavior based on their personality.
Advanced Computing in Industrial Mathematics, 2018
The solution, obtained in the environment of finite precision machine arithmetic must be allays a... more The solution, obtained in the environment of finite precision machine arithmetic must be allays accompanied by an analysis of the conditioning of the problem solved. The perturbation analysis derives measures for the sensitivity of the solution to perturbations in the matrix coefficients. Motivated by these, in order to ascertain the accuracy of an iteratively calculated solution to a nonlinear matrix equation arising in Tree-like stochastic processes, in this paper norm-wise, mixed and component-wise condition numbers, as well as local perturbation bounds are formulated and norm-wise non-local residual bounds are derived using the methods of nonlinear perturbation analysis (Frechet derivatives, Lyapunov majorants, fixed-point principles). The residual bounds are formulated in terms of the computed approximate solution to the equation and can be used as a stop criteria of the iterations, when solving the considered nonlinear matrix equation by a numerically stable iterative algorithm.
In this paper a local perturbation analysis of the stochastic matrix Riccati equation /SMRE/ with... more In this paper a local perturbation analysis of the stochastic matrix Riccati equation /SMRE/ with applications in linear quadratic optimization of stochastic finance models is made. Rewriting the SMRE in equivalent form of affine linear operators and applying the techniques of Frechet derivatives, absolute and relative norm-wise condition numbers are derived and local (first order) perturbation bounds for the error in the computed solution are formulated. The condition numbers and the perturbation bounds allow to estimate the conditioning of the SMRE and the accuracy of its computed by a numerical stable algorithm solution.
The paper deals with the existing methods for estimating the sensitivity of the solution to the n... more The paper deals with the existing methods for estimating the sensitivity of the solution to the nonlinear matrix equation Q
Nonsymmetric differential matrix Riccati equations arise in many problems related to science and ... more Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approaches of nonlocal perturbation analysis of the symmetric differential Riccati equation are extended to the nonsymmetric case. Applying the techniques of Fréchet derivatives, Lyapunov majorants and fixed-point principle, two perturbation bounds are derived: the first one is based on the integral form of the solution and the second one considers the equivalent solution to the initial value problem of the associated differential system. The first bound is derived for the nonsymmetric differential Riccati equation in its general form. The perturbation bound based on the sensitivity analysis of the associated linear differential system is formulated for the low-dimensional approximate solution to the large-scale nonsymmetric differential Riccati...
In this paper the problem of optimal pole assignment of linear time{invariant multi{input systems... more In this paper the problem of optimal pole assignment of linear time{invariant multi{input systems is considered. A direct parametrization of the solution for low{dimensional system is presented.
The paper deals with the perturbation estimates proposed by S. Xu [Linear Algebra Appl. 336, No. ... more The paper deals with the perturbation estimates proposed by S. Xu [Linear Algebra Appl. 336, No. 1–3, 61–70 (2001; Zbl 0992.15013)], J.-G. Sun and S. Xu [ibid. 362, 211–228 (2003; Zbl 1020.15012)] and M. M. Konstantinov et al. [in: Proceedings of the jubilee scientific conference of the University of Architecture, Civil Engineering and Geodesy on the occasion of the 60th anniversary of its foundation, Sofia, Bulgaria, November 2002. Vol. 8: Geodesy, transportation engineering, geotechnics, mathematics, physics. Sofia: University of Architecture, Civil Engineering and Geodesy. 495–504 (2002; Zbl 1187.15020)] for evaluating the sensitivity of the solution to the complex fractional-affine matrix equation X=A 1 +A 2 H X -1 A 2 relative to rounding and parameter errors. The effectiveness and reliability of the different methods are analyzed by experiments with numerical examples.
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Papers by Vera Angelova