Vera Angelova - Academia.edu (original) (raw)

Papers by Vera Angelova

Research paper thumbnail of On the Sensitivity Estimation of the Matrix Equation

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

Research paper thumbnail of Residual bounds of the nonlinear matrix equation X + A*F(X)A = Q

International Journal of Data Science, 2016

In this paper, we consider the nonlinear matrix equation X + A * F (X)A = Q and we derive norm-wi... more In this paper, we consider the nonlinear matrix equation X + A * F (X)A = Q and we derive norm-wise non-local residual bounds for the accuracy of the solution obtained by an iterative algorithm. The residual bounds are derived using the method of Lyapunov majorants and the techniques of the fixed point principle. Two particular cases of the equation are considered in details and explicit expressions of the norm-wise non-local residual bounds are obtained as well. Numerical examples for the two, considered in the paper different cases of the nonlinear matrix function F (X) are provided to demonstrate the efficiency of the bounds proposed.

Research paper thumbnail of Improved residual bound of the matrix equation $ X + A_2\He X^{-1}A_2 = A_1$

Research paper thumbnail of The pole assignment problem-parametrization of the solution for low dimensional systems

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.

Research paper thumbnail of Comparison of perturbation bounds for the matrix equation X=A 1 +A 2 H X -1 A 2

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.

Research paper thumbnail of On the Sensitivity Estimation of the Matrix Differential Riccati Equation

The paper deals with the estimates proposed by Kenney, Hewer and Konstantinov, Pelova 6] for eval... more The paper deals with the estimates proposed by Kenney, Hewer and Konstantinov, Pelova 6] for evaluating the sensitivity of the solution to diierential matrix Ric-cati equations relative to rounding and parameter errors. The eeectiveness and the reliability o f the two methods are analyzed by experiments with a reference model.

Research paper thumbnail of On the Sensitivity Estimation of the Matrix Equation * Q A X A X t s

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 A X A X t s = ± * , with s and t – real numbers. The perturbation bounds for the complex matrix equation proposed by Yin, Liu, Fang in [9] and Yin, Liu in [8], when s is a positive and t is a negative integers and by Li, Zhang in [6], when s=1, 0) 1, [− ∈ t , as well as the estimates proposed by Jia, Wei in [4] for the real equation with s and t – non negative integers and the perturbation bounds proposed by Konstantinov et al. in [5] for the real and complex equation with s and t real numbers are considered. The effectiveness and the reliability of the perturbation bounds are analysed by several numerical examples with reference models based on Example 1 from [3] and Example 2 from [2].

Research paper thumbnail of Sensitivity of the matrix equation A 0 +∑ i=1 k σ i A 1 * X p i A i =0,σ i =±1

Applied and computational mathematics

In this paper, the sensitivity of the solution to the general nonlinear matrix equation A 0 +∑ i=... more In this paper, the sensitivity of the solution to the general nonlinear matrix equation A 0 +∑ i=1 k σ i A 1 * X p i A i =0,σ i =±1, is studied, where k is a positive integer, and p i (i=i=11,2,...k) are real numbers. Using the technique of Fréchet derivatives, the perturbed equation is written as an equivalent operator equation, which allows applying the method of Lyapunov majorants and Schauder fixed point principle to obtain norm-wise condition numbers, as well as local and nonlocal perturbation bounds. Several numerical examples are given to illustrate the effectiveness of the perturbation bounds.

Research paper thumbnail of Condition numbers for the matrix equation X+A H X -1 A+B H X -1 B=I

Comptes rendus de l'Académie bulgare des sciences: sciences mathématiques et naturelles

The paper is devoted to the conditioning of the nonlinear complex matrix equation X + A^H X^{−1}A... more The paper is devoted to the conditioning of the nonlinear complex matrix equation X + A^H X^{−1}A + B^H X^{−1}B = I with square data matrices A and B (AH denotes the complex conjugate transpose of the matrix A) and I being the identity matrix. This equation arises when systems of linear equations by matrix decomposition are solved. Based on the perturbation analysis, upper bounds for the norm-wise, mixed and component-wise condition numbers are obtained. The results are illustrated by numerical examples.

Research paper thumbnail of Perturbation bounds for the matrix equation C+∑ i=1 r A i XB i +DX s E=0

Comptes rendus de l'Académie bulgare des sciences: sciences mathématiques et naturelles

Research paper thumbnail of Conditioning and sensitivity of the difference matrix Riccati equation

Proceedings of 1995 American Control Conference - ACC'95

The paper presents a local and nonlocal perturbation analysis of the difference matrix Riccati eq... more The paper presents a local and nonlocal perturbation analysis of the difference matrix Riccati equation. The conditioning of the equation is determined in particular

Research paper thumbnail of Improved perturbation bounds for the matrix exponential

Lecture Notes in Computer Science, 1997

Univ. of Arch. & Civil Eng.,1 Hr.Smirnenski Blv.,1421 Sofia, Bulgaria, mmk_f te@bgace5, uacg.... more Univ. of Arch. & Civil Eng.,1 Hr.Smirnenski Blv.,1421 Sofia, Bulgaria, mmk_f te@bgace5, uacg. acad. bg 2 Dept. of Automatics, Technical Univ. of Sofia, 1756 Sofia, Bulgaria 3 IIT, BAS, Akad. G. Bonchev Str., B1.2, 1113 Sofia, Bulgaria, popchev@bgcict, acad. bg

Research paper thumbnail of Perturbation analysis of fractional affine matrix equations

ABSTRACT Local and non-local perturbation bounds for general fractional aane matrix algebraic equ... more ABSTRACT Local and non-local perturbation bounds for general fractional aane matrix algebraic equations are derived using the technique of Lyapunov majorants and point principles.

Research paper thumbnail of Perturbation Bounds for X-A1-ΣAH 2 X-NA2= 0

PERTURBATION BOUNDS FOR X -A1 -σAH 2 X-NA2 = 0 Mihail Mihaylov Konstantinov* Petko Hristov Petkov... more PERTURBATION BOUNDS FOR X -A1 -σAH 2 X-NA2 = 0 Mihail Mihaylov Konstantinov* Petko Hristov Petkov** Vera Angelova Angelova*** Ivan Petkov Popchev*** ... 1046 Sofia, Bulgaria e-mail: mmk-fte@uacg.bg **Department of Automatics, Technical University of Sofia

Research paper thumbnail of Predicting User Behavior in e-Commerce Using Machine Learning

Cybernetics and Information Technologies

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.

Research paper thumbnail of IICT-BAS Statistique inférentielle

Research paper thumbnail of IICT-BAS Eléments de la théorie des probabilités

The series Lectures Notes in Computer Science and Technologies of the Institute of Information an... more The series Lectures Notes in Computer Science and Technologies of the Institute of Information and Communication Technologies at the Bulgarian Academy of Sciences presents in an electronic format textbooks for undergraduate, graduate and PhD students studied various programs related to Informatics, Computational Mathematics, Mathematical Modeling, Communication Technologies, etc., as well as for all readers interested in these scientific disciplines. The Lecture Notes are based on courses taught by scientists of the Institute of Information and Communication Technologies-BAS in various Bulgarian universities and the Center for Doctoral Training in BAS. The published materials are with open access-they are freely available without any charge.

Research paper thumbnail of IICT-BAS Statistique descriptive

The series Lectures Notes in Computer Science and Technologies of the Institute of Information an... more The series Lectures Notes in Computer Science and Technologies of the Institute of Information and Communication Technologies at the Bulgarian Academy of Sciences presents in an electronic format textbooks for undergraduate, graduate and PhD students studied various programs related to Informatics, Computational Mathematics, Mathematical Modeling, Communication Technologies, etc., as well as for all readers interested in these scientific disciplines. The Lecture Notes are based on courses taught by scientists of the Institute of Information and Communication Technologies-BAS in various Bulgarian universities and the Center for Doctoral Training in BAS. The published materials are with open access-they are freely available without any charge.

Research paper thumbnail of Approximate solutions to large nonsymmetric differential Riccati problems with applications to transport theory

Numerical Linear Algebra with Applications, 2019

SummaryIn this paper, we consider large‐scale nonsymmetric differential matrix Riccati equations ... more SummaryIn this paper, we consider large‐scale nonsymmetric differential matrix Riccati equations with low‐rank right‐hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability, and others. We show how to apply Krylov‐type methods such as the extended block Arnoldi algorithm to get low‐rank approximate solutions. The initial problem is projected onto small subspaces to get low dimensional nonsymmetric differential equations that are solved using the exponential approximation or via other integration schemes such as backward differentiation formula (BDF) or Rosenbrock method. We also show how these techniques can be easily used to solve some problems from the well‐known transport equation. Some numerical examples are given to illustrate the application of the proposed methods to large‐scale problems.

Research paper thumbnail of Perturbation analysis of difference matrix Riccati equation

Research paper thumbnail of On the Sensitivity Estimation of the Matrix Equation

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

Research paper thumbnail of Residual bounds of the nonlinear matrix equation X + A*F(X)A = Q

International Journal of Data Science, 2016

In this paper, we consider the nonlinear matrix equation X + A * F (X)A = Q and we derive norm-wi... more In this paper, we consider the nonlinear matrix equation X + A * F (X)A = Q and we derive norm-wise non-local residual bounds for the accuracy of the solution obtained by an iterative algorithm. The residual bounds are derived using the method of Lyapunov majorants and the techniques of the fixed point principle. Two particular cases of the equation are considered in details and explicit expressions of the norm-wise non-local residual bounds are obtained as well. Numerical examples for the two, considered in the paper different cases of the nonlinear matrix function F (X) are provided to demonstrate the efficiency of the bounds proposed.

Research paper thumbnail of Improved residual bound of the matrix equation $ X + A_2\He X^{-1}A_2 = A_1$

Research paper thumbnail of The pole assignment problem-parametrization of the solution for low dimensional systems

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.

Research paper thumbnail of Comparison of perturbation bounds for the matrix equation X=A 1 +A 2 H X -1 A 2

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.

Research paper thumbnail of On the Sensitivity Estimation of the Matrix Differential Riccati Equation

The paper deals with the estimates proposed by Kenney, Hewer and Konstantinov, Pelova 6] for eval... more The paper deals with the estimates proposed by Kenney, Hewer and Konstantinov, Pelova 6] for evaluating the sensitivity of the solution to diierential matrix Ric-cati equations relative to rounding and parameter errors. The eeectiveness and the reliability o f the two methods are analyzed by experiments with a reference model.

Research paper thumbnail of On the Sensitivity Estimation of the Matrix Equation * Q A X A X t s

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 A X A X t s = ± * , with s and t – real numbers. The perturbation bounds for the complex matrix equation proposed by Yin, Liu, Fang in [9] and Yin, Liu in [8], when s is a positive and t is a negative integers and by Li, Zhang in [6], when s=1, 0) 1, [− ∈ t , as well as the estimates proposed by Jia, Wei in [4] for the real equation with s and t – non negative integers and the perturbation bounds proposed by Konstantinov et al. in [5] for the real and complex equation with s and t real numbers are considered. The effectiveness and the reliability of the perturbation bounds are analysed by several numerical examples with reference models based on Example 1 from [3] and Example 2 from [2].

Research paper thumbnail of Sensitivity of the matrix equation A 0 +∑ i=1 k σ i A 1 * X p i A i =0,σ i =±1

Applied and computational mathematics

In this paper, the sensitivity of the solution to the general nonlinear matrix equation A 0 +∑ i=... more In this paper, the sensitivity of the solution to the general nonlinear matrix equation A 0 +∑ i=1 k σ i A 1 * X p i A i =0,σ i =±1, is studied, where k is a positive integer, and p i (i=i=11,2,...k) are real numbers. Using the technique of Fréchet derivatives, the perturbed equation is written as an equivalent operator equation, which allows applying the method of Lyapunov majorants and Schauder fixed point principle to obtain norm-wise condition numbers, as well as local and nonlocal perturbation bounds. Several numerical examples are given to illustrate the effectiveness of the perturbation bounds.

Research paper thumbnail of Condition numbers for the matrix equation X+A H X -1 A+B H X -1 B=I

Comptes rendus de l'Académie bulgare des sciences: sciences mathématiques et naturelles

The paper is devoted to the conditioning of the nonlinear complex matrix equation X + A^H X^{−1}A... more The paper is devoted to the conditioning of the nonlinear complex matrix equation X + A^H X^{−1}A + B^H X^{−1}B = I with square data matrices A and B (AH denotes the complex conjugate transpose of the matrix A) and I being the identity matrix. This equation arises when systems of linear equations by matrix decomposition are solved. Based on the perturbation analysis, upper bounds for the norm-wise, mixed and component-wise condition numbers are obtained. The results are illustrated by numerical examples.

Research paper thumbnail of Perturbation bounds for the matrix equation C+∑ i=1 r A i XB i +DX s E=0

Comptes rendus de l'Académie bulgare des sciences: sciences mathématiques et naturelles

Research paper thumbnail of Conditioning and sensitivity of the difference matrix Riccati equation

Proceedings of 1995 American Control Conference - ACC'95

The paper presents a local and nonlocal perturbation analysis of the difference matrix Riccati eq... more The paper presents a local and nonlocal perturbation analysis of the difference matrix Riccati equation. The conditioning of the equation is determined in particular

Research paper thumbnail of Improved perturbation bounds for the matrix exponential

Lecture Notes in Computer Science, 1997

Univ. of Arch. & Civil Eng.,1 Hr.Smirnenski Blv.,1421 Sofia, Bulgaria, mmk_f te@bgace5, uacg.... more Univ. of Arch. & Civil Eng.,1 Hr.Smirnenski Blv.,1421 Sofia, Bulgaria, mmk_f te@bgace5, uacg. acad. bg 2 Dept. of Automatics, Technical Univ. of Sofia, 1756 Sofia, Bulgaria 3 IIT, BAS, Akad. G. Bonchev Str., B1.2, 1113 Sofia, Bulgaria, popchev@bgcict, acad. bg

Research paper thumbnail of Perturbation analysis of fractional affine matrix equations

ABSTRACT Local and non-local perturbation bounds for general fractional aane matrix algebraic equ... more ABSTRACT Local and non-local perturbation bounds for general fractional aane matrix algebraic equations are derived using the technique of Lyapunov majorants and point principles.

Research paper thumbnail of Perturbation Bounds for X-A1-ΣAH 2 X-NA2= 0

PERTURBATION BOUNDS FOR X -A1 -σAH 2 X-NA2 = 0 Mihail Mihaylov Konstantinov* Petko Hristov Petkov... more PERTURBATION BOUNDS FOR X -A1 -σAH 2 X-NA2 = 0 Mihail Mihaylov Konstantinov* Petko Hristov Petkov** Vera Angelova Angelova*** Ivan Petkov Popchev*** ... 1046 Sofia, Bulgaria e-mail: mmk-fte@uacg.bg **Department of Automatics, Technical University of Sofia

Research paper thumbnail of Predicting User Behavior in e-Commerce Using Machine Learning

Cybernetics and Information Technologies

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.

Research paper thumbnail of IICT-BAS Statistique inférentielle

Research paper thumbnail of IICT-BAS Eléments de la théorie des probabilités

The series Lectures Notes in Computer Science and Technologies of the Institute of Information an... more The series Lectures Notes in Computer Science and Technologies of the Institute of Information and Communication Technologies at the Bulgarian Academy of Sciences presents in an electronic format textbooks for undergraduate, graduate and PhD students studied various programs related to Informatics, Computational Mathematics, Mathematical Modeling, Communication Technologies, etc., as well as for all readers interested in these scientific disciplines. The Lecture Notes are based on courses taught by scientists of the Institute of Information and Communication Technologies-BAS in various Bulgarian universities and the Center for Doctoral Training in BAS. The published materials are with open access-they are freely available without any charge.

Research paper thumbnail of IICT-BAS Statistique descriptive

The series Lectures Notes in Computer Science and Technologies of the Institute of Information an... more The series Lectures Notes in Computer Science and Technologies of the Institute of Information and Communication Technologies at the Bulgarian Academy of Sciences presents in an electronic format textbooks for undergraduate, graduate and PhD students studied various programs related to Informatics, Computational Mathematics, Mathematical Modeling, Communication Technologies, etc., as well as for all readers interested in these scientific disciplines. The Lecture Notes are based on courses taught by scientists of the Institute of Information and Communication Technologies-BAS in various Bulgarian universities and the Center for Doctoral Training in BAS. The published materials are with open access-they are freely available without any charge.

Research paper thumbnail of Approximate solutions to large nonsymmetric differential Riccati problems with applications to transport theory

Numerical Linear Algebra with Applications, 2019

SummaryIn this paper, we consider large‐scale nonsymmetric differential matrix Riccati equations ... more SummaryIn this paper, we consider large‐scale nonsymmetric differential matrix Riccati equations with low‐rank right‐hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability, and others. We show how to apply Krylov‐type methods such as the extended block Arnoldi algorithm to get low‐rank approximate solutions. The initial problem is projected onto small subspaces to get low dimensional nonsymmetric differential equations that are solved using the exponential approximation or via other integration schemes such as backward differentiation formula (BDF) or Rosenbrock method. We also show how these techniques can be easily used to solve some problems from the well‐known transport equation. Some numerical examples are given to illustrate the application of the proposed methods to large‐scale problems.

Research paper thumbnail of Perturbation analysis of difference matrix Riccati equation