Stoil Ivanov | University of Plovdiv (original) (raw)

Papers by Stoil Ivanov

Research paper thumbnail of Families of high-order simultaneous methods with several corrections

Numerical Algorithms, Jan 5, 2024

Research paper thumbnail of A new family of Sakurai–Torii–Sugiura type iterative methods with high order of convergence

Journal of Computational and Applied Mathematics

In this paper, we introduce a new family of iterative methods for finding simultaneously all zero... more In this paper, we introduce a new family of iterative methods for finding simultaneously all zeros (multiple or simple) of a polynomial. The proposed family is constructed by combining the known Sakurai–Torii–Sugiura iteration function with an arbitrary iteration function. We provide a detailed convergence analysis in the following two directions: local convergence if the polynomial has multiple zeros with known multiplicity and semilocal convergence if the polynomial has only simple zeros. As an application, we study the convergence of several particular iterative methods with high order of convergence.

Research paper thumbnail of A New Random Positioning Machine Modification Applied for Microgravity Simulation in Laboratory Experiments with Rats

Research paper thumbnail of Local Convergence Analysis of a One Parameter Family of Simultaneous Methods with Applications to Real-World Problems

Algorithms

In this paper, we provide a detailed local convergence analysis of a one-parameter family of iter... more In this paper, we provide a detailed local convergence analysis of a one-parameter family of iteration methods for the simultaneous approximation of polynomial zeros due to Ivanov (Numer. Algor. 75(4): 1193–1204, 2017). Thus, we obtain two local convergence theorems that provide sufficient conditions to guarantee the Q-cubic convergence of all members of the family. Among the other contributions, our results unify the latest such kind of results of the well known Dochev–Byrnev and Ehrlich methods. Several practical applications are further given to emphasize the advantages of the studied family of methods and to show the applicability of the theoretical results.

Research paper thumbnail of On the semilocal convergence of a modified weierstrass method for the simultaneous computation of polynomial zeros

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020, 2022

Research paper thumbnail of A general approach to the study of the convergence of Picard iteration with an application to Halley's method for multiple zeros of analytic functions

Journal of Mathematical Analysis and Applications

Research paper thumbnail of On the geodesics in Bondi-Gold-Hoyle universe model

In this paper we first derive the geodesic equations in the Bondi-Gold-Hoyle universe model and t... more In this paper we first derive the geodesic equations in the Bondi-Gold-Hoyle universe model and then we provide exact analytical solutions of these equations. The obtained solutions describe the motion of the massless particles in the considered universe model.

Research paper thumbnail of General Local Convergence Theorems about the Picard Iteration in Arbitrary Normed Fields with Applications to Super–Halley Method for Multiple Polynomial Zeros

Mathematics, 2020

In this paper, we prove two general convergence theorems with error estimates that give sufficien... more In this paper, we prove two general convergence theorems with error estimates that give sufficient conditions to guarantee the local convergence of the Picard iteration in arbitrary normed fields. Thus, we provide a unified approach for investigating the local convergence of Picard-type iterative methods for simple and multiple roots of nonlinear equations. As an application, we prove two new convergence theorems with a priori and a posteriori error estimates about the Super-Halley method for multiple polynomial zeros.

Research paper thumbnail of A Theorem for Local Convergence of Schrӧder ’ S Method for Simultaneous Finding Polynomial Zeros of Unknown Multiplicity

In this note we present a local convergence theorem for Schrӧder's iterative method considere... more In this note we present a local convergence theorem for Schrӧder's iterative method considered as a method for simultaneous finding polynomial zeros of unknown multiplicity. Error estimate is also provided.

Research paper thumbnail of On the convergence of Schröder’s method for the simultaneous computation of polynomial zeros of unknown multiplicity

Calcolo, 2017

In this paper, we establish a general theorem for iteration functions in a cone normed space over... more In this paper, we establish a general theorem for iteration functions in a cone normed space over R n. Using this theorem together with a general convergence theorem of Proinov (J Complex 33:118-144, 2016), we obtain a local convergence theorem with a priori and a posteriori error estimates as well as a theorem under computationally verifiable initial conditions for the Schröder's iterative method considered as a method for simultaneous computation of polynomial zeros of unknown multiplicity. Numerical examples which demonstrate the convergence properties of the proposed method are also provided.

Research paper thumbnail of A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously

Numerical Algorithms, 2016

In this paper, we first present a family of iterative algorithms for simultaneous determination o... more In this paper, we first present a family of iterative algorithms for simultaneous determination of all zeros of a polynomial. This family contains two well-known algorithms: Dochev-Byrnev's method and Ehrlich's method. Second, using Proinov's approach to studying convergence of iterative methods for polynomial zeros, we provide a semilocal convergence theorem that unifies the results of Proinov (Appl. Math. Comput. 284: 102-114, 2016) for Dochev-Byrnev's and Ehrlich's methods.

Research paper thumbnail of Convergence of Newton, Halley and Chebyshev iterative methods as methods for simultaneous determination of multiple polynomial zeros

Applied Numerical Mathematics, 2017

Abstract In this paper, we provide a local convergence analysis of Newton, Halley and Chebyshev i... more Abstract In this paper, we provide a local convergence analysis of Newton, Halley and Chebyshev iterative methods considered as methods for simultaneous determination of all multiple zeros of a polynomial f over an arbitrary normed field K . Convergence theorems with a priori and a posteriori error estimates for each of the proposed methods are established. The obtained results for Newton and Chebyshev methods are new even in the case of simple zeros. Three numerical examples are given to compare the convergence properties of the considered methods and to confirm the theoretical results.

Research paper thumbnail of On the Convergence of Chebyshev’s Method for Multiple Polynomial Zeros

Results in Mathematics, 2015

In this paper we investigate the local convergence of Chebyshev's iterative method for the comput... more In this paper we investigate the local convergence of Chebyshev's iterative method for the computation of a multiple polynomial zero. We establish two convergence theorems for polynomials over an arbitrary normed field. A priori and a posteriori error estimates are also provided. All of the results are new even in the case of simple zero.

Research paper thumbnail of Convergence of Halley’s iterative method for individual and simultaneous approximation of polynomial zeros (in Bulgarian)

In this work we investigate the convergence of Halley’s method for individual and simultaneous ap... more In this work we investigate the convergence of Halley’s method for individual and simultaneous approximation of polynomial zeros. Also we study the convergence of Halley’s method for multiple polynomial zeros and Schröder’s method for polynomial zeros with unknown multiplicity. We present two types of local convergence theorems with error estimates for Halley’s method for multiple polynomial zeros. All of the results are new even in the case of simple zeros. We establish two types of local convergence theorems with error estimates for Schröder's method for polynomial zeros with unknown multiplicity. For the first time the classical Halley’s method is considered as a method for finding all zeros of a polynomial simultaneously. Two types of local convergence theorems for Halley's method as a method for simultaneous approximation of polynomial zeros are presented. We also present a convergence theorem for Halley's method under computationally verifiable initial conditions. ...

Research paper thumbnail of Non-universal critical properties of the ferromagnetic mean spherical model with long-range interaction

The bulk critical behavior of the mean spherical model with long-range interaction (decaying at l... more The bulk critical behavior of the mean spherical model with long-range interaction (decaying at large distances r as r −d−σ , where d is the space dimensionality and 0 < σ ≤ 2) is studied at the upper critical dimension by using the properties of the Lambert W-function. Exact expressions for the spherical field, the free energy density and the specific heat per spin are presented. The exact results are compared with the asymptotic ones on the basis of the calculated absolute and relative errors. Asymptotic analytical expressions for the absolute errors are also provided. It is shown that the obtained results are valid in a broader neighborhood of the critical point.

Research paper thumbnail of On the convergence of Halley’s method for simultaneous computation of polynomial zeros

Journal of Numerical Mathematics, 2015

In this paper we study the convergence of Halley’s method as a method for finding all zeros of a ... more In this paper we study the convergence of Halley’s method as a method for finding all zeros of a polynomial simultaneously. We present two types of local convergence theorems as well as a semilocal convergence theorem for Halley’s method for simultaneous computation of polynomial zeros.

Research paper thumbnail of On the critical specific heat capacity of a classical anharmonic crystal with long-range interaction

Journal of Physics: Conference Series, 2014

The bulk critical specific heat capacity of a classical anharmonic crystal with long-range intera... more The bulk critical specific heat capacity of a classical anharmonic crystal with long-range interaction (decreasing at large distances r as r −d−σ , where d is the space dimensionality and 0 < σ ≤ 2) is studied. An exact analytical expression is obtained at the upper critical dimension d = 2σ of the system. This result depends on both the deviation from the critical point and the space dimensionality of the system, while the known asymptotic one depends only on the deviation from the critical point. For real systems (chains, thin layers, i.e. films and three-dimensional systems) the exact result and the asymptotic one are graphically presented and compared on the basis of the calculated relative errors. The obtained result holds true in a broader neighborhood of the critical point. The expansion of the critical region is estimated at the three real physical dimensionalities.

Research paper thumbnail of A Theorem for Local Convergence of Halley’s Method for Finding Polynomial Zeros Simultaneously

In this note we present a local convergence theorem of Halley's iterative method considered a... more In this note we present a local convergence theorem of Halley's iterative method considered as a method for finding all zeros of a polynomial simultaneously. The main result is based on a new local convergence theory for iterative processes published in 2009 by the first author.

Research paper thumbnail of On the Critical Behavior of the Inverse Susceptibility of a Model of Structural Phase Transitions

An exactly solvable lattice model describing structural phase transitions in an anharmonic crysta... more An exactly solvable lattice model describing structural phase transitions in an anharmonic crystal with long-range interaction is considered in the neighborhoods of the quantum and classical critical points at the corresponding upper critical dimensions. In a broader neighborhood of the critical region the inverse susceptibility of the model is exactly calculated in terms of the Lambert W-function and graphically presented as a function of the deviation from the critical point and the upper critical dimension. For quantum and classical systems with real physical dimensions (chains, thin layers and three-dimensional systems) the exact results are compared with the asymptotic ones on the basis of some numerical data for their ratio. Relative errors are also provided.

Research paper thumbnail of On the Convergence of Halley’s Method for Multiple Polynomial Zeros

Mediterranean Journal of Mathematics, 2014

In this paper, we investigate the local convergence of Halley's method for the computation of a m... more In this paper, we investigate the local convergence of Halley's method for the computation of a multiple polynomial zero with known multiplicity. We establish two local convergence theorems for Halley's method for multiple polynomial zeros under different initial conditions. The convergence of these results is cubic right from the first iteration. Also we find an initial condition which guarantees that an initial guess is an approximate zero of the second kind for Halley's method. All of the results are new even in the case of simple zeros.

Research paper thumbnail of Families of high-order simultaneous methods with several corrections

Numerical Algorithms, Jan 5, 2024

Research paper thumbnail of A new family of Sakurai–Torii–Sugiura type iterative methods with high order of convergence

Journal of Computational and Applied Mathematics

In this paper, we introduce a new family of iterative methods for finding simultaneously all zero... more In this paper, we introduce a new family of iterative methods for finding simultaneously all zeros (multiple or simple) of a polynomial. The proposed family is constructed by combining the known Sakurai–Torii–Sugiura iteration function with an arbitrary iteration function. We provide a detailed convergence analysis in the following two directions: local convergence if the polynomial has multiple zeros with known multiplicity and semilocal convergence if the polynomial has only simple zeros. As an application, we study the convergence of several particular iterative methods with high order of convergence.

Research paper thumbnail of A New Random Positioning Machine Modification Applied for Microgravity Simulation in Laboratory Experiments with Rats

Research paper thumbnail of Local Convergence Analysis of a One Parameter Family of Simultaneous Methods with Applications to Real-World Problems

Algorithms

In this paper, we provide a detailed local convergence analysis of a one-parameter family of iter... more In this paper, we provide a detailed local convergence analysis of a one-parameter family of iteration methods for the simultaneous approximation of polynomial zeros due to Ivanov (Numer. Algor. 75(4): 1193–1204, 2017). Thus, we obtain two local convergence theorems that provide sufficient conditions to guarantee the Q-cubic convergence of all members of the family. Among the other contributions, our results unify the latest such kind of results of the well known Dochev–Byrnev and Ehrlich methods. Several practical applications are further given to emphasize the advantages of the studied family of methods and to show the applicability of the theoretical results.

Research paper thumbnail of On the semilocal convergence of a modified weierstrass method for the simultaneous computation of polynomial zeros

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020, 2022

Research paper thumbnail of A general approach to the study of the convergence of Picard iteration with an application to Halley's method for multiple zeros of analytic functions

Journal of Mathematical Analysis and Applications

Research paper thumbnail of On the geodesics in Bondi-Gold-Hoyle universe model

In this paper we first derive the geodesic equations in the Bondi-Gold-Hoyle universe model and t... more In this paper we first derive the geodesic equations in the Bondi-Gold-Hoyle universe model and then we provide exact analytical solutions of these equations. The obtained solutions describe the motion of the massless particles in the considered universe model.

Research paper thumbnail of General Local Convergence Theorems about the Picard Iteration in Arbitrary Normed Fields with Applications to Super–Halley Method for Multiple Polynomial Zeros

Mathematics, 2020

In this paper, we prove two general convergence theorems with error estimates that give sufficien... more In this paper, we prove two general convergence theorems with error estimates that give sufficient conditions to guarantee the local convergence of the Picard iteration in arbitrary normed fields. Thus, we provide a unified approach for investigating the local convergence of Picard-type iterative methods for simple and multiple roots of nonlinear equations. As an application, we prove two new convergence theorems with a priori and a posteriori error estimates about the Super-Halley method for multiple polynomial zeros.

Research paper thumbnail of A Theorem for Local Convergence of Schrӧder ’ S Method for Simultaneous Finding Polynomial Zeros of Unknown Multiplicity

In this note we present a local convergence theorem for Schrӧder's iterative method considere... more In this note we present a local convergence theorem for Schrӧder's iterative method considered as a method for simultaneous finding polynomial zeros of unknown multiplicity. Error estimate is also provided.

Research paper thumbnail of On the convergence of Schröder’s method for the simultaneous computation of polynomial zeros of unknown multiplicity

Calcolo, 2017

In this paper, we establish a general theorem for iteration functions in a cone normed space over... more In this paper, we establish a general theorem for iteration functions in a cone normed space over R n. Using this theorem together with a general convergence theorem of Proinov (J Complex 33:118-144, 2016), we obtain a local convergence theorem with a priori and a posteriori error estimates as well as a theorem under computationally verifiable initial conditions for the Schröder's iterative method considered as a method for simultaneous computation of polynomial zeros of unknown multiplicity. Numerical examples which demonstrate the convergence properties of the proposed method are also provided.

Research paper thumbnail of A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously

Numerical Algorithms, 2016

In this paper, we first present a family of iterative algorithms for simultaneous determination o... more In this paper, we first present a family of iterative algorithms for simultaneous determination of all zeros of a polynomial. This family contains two well-known algorithms: Dochev-Byrnev's method and Ehrlich's method. Second, using Proinov's approach to studying convergence of iterative methods for polynomial zeros, we provide a semilocal convergence theorem that unifies the results of Proinov (Appl. Math. Comput. 284: 102-114, 2016) for Dochev-Byrnev's and Ehrlich's methods.

Research paper thumbnail of Convergence of Newton, Halley and Chebyshev iterative methods as methods for simultaneous determination of multiple polynomial zeros

Applied Numerical Mathematics, 2017

Abstract In this paper, we provide a local convergence analysis of Newton, Halley and Chebyshev i... more Abstract In this paper, we provide a local convergence analysis of Newton, Halley and Chebyshev iterative methods considered as methods for simultaneous determination of all multiple zeros of a polynomial f over an arbitrary normed field K . Convergence theorems with a priori and a posteriori error estimates for each of the proposed methods are established. The obtained results for Newton and Chebyshev methods are new even in the case of simple zeros. Three numerical examples are given to compare the convergence properties of the considered methods and to confirm the theoretical results.

Research paper thumbnail of On the Convergence of Chebyshev’s Method for Multiple Polynomial Zeros

Results in Mathematics, 2015

In this paper we investigate the local convergence of Chebyshev's iterative method for the comput... more In this paper we investigate the local convergence of Chebyshev's iterative method for the computation of a multiple polynomial zero. We establish two convergence theorems for polynomials over an arbitrary normed field. A priori and a posteriori error estimates are also provided. All of the results are new even in the case of simple zero.

Research paper thumbnail of Convergence of Halley’s iterative method for individual and simultaneous approximation of polynomial zeros (in Bulgarian)

In this work we investigate the convergence of Halley’s method for individual and simultaneous ap... more In this work we investigate the convergence of Halley’s method for individual and simultaneous approximation of polynomial zeros. Also we study the convergence of Halley’s method for multiple polynomial zeros and Schröder’s method for polynomial zeros with unknown multiplicity. We present two types of local convergence theorems with error estimates for Halley’s method for multiple polynomial zeros. All of the results are new even in the case of simple zeros. We establish two types of local convergence theorems with error estimates for Schröder's method for polynomial zeros with unknown multiplicity. For the first time the classical Halley’s method is considered as a method for finding all zeros of a polynomial simultaneously. Two types of local convergence theorems for Halley's method as a method for simultaneous approximation of polynomial zeros are presented. We also present a convergence theorem for Halley's method under computationally verifiable initial conditions. ...

Research paper thumbnail of Non-universal critical properties of the ferromagnetic mean spherical model with long-range interaction

The bulk critical behavior of the mean spherical model with long-range interaction (decaying at l... more The bulk critical behavior of the mean spherical model with long-range interaction (decaying at large distances r as r −d−σ , where d is the space dimensionality and 0 < σ ≤ 2) is studied at the upper critical dimension by using the properties of the Lambert W-function. Exact expressions for the spherical field, the free energy density and the specific heat per spin are presented. The exact results are compared with the asymptotic ones on the basis of the calculated absolute and relative errors. Asymptotic analytical expressions for the absolute errors are also provided. It is shown that the obtained results are valid in a broader neighborhood of the critical point.

Research paper thumbnail of On the convergence of Halley’s method for simultaneous computation of polynomial zeros

Journal of Numerical Mathematics, 2015

In this paper we study the convergence of Halley’s method as a method for finding all zeros of a ... more In this paper we study the convergence of Halley’s method as a method for finding all zeros of a polynomial simultaneously. We present two types of local convergence theorems as well as a semilocal convergence theorem for Halley’s method for simultaneous computation of polynomial zeros.

Research paper thumbnail of On the critical specific heat capacity of a classical anharmonic crystal with long-range interaction

Journal of Physics: Conference Series, 2014

The bulk critical specific heat capacity of a classical anharmonic crystal with long-range intera... more The bulk critical specific heat capacity of a classical anharmonic crystal with long-range interaction (decreasing at large distances r as r −d−σ , where d is the space dimensionality and 0 < σ ≤ 2) is studied. An exact analytical expression is obtained at the upper critical dimension d = 2σ of the system. This result depends on both the deviation from the critical point and the space dimensionality of the system, while the known asymptotic one depends only on the deviation from the critical point. For real systems (chains, thin layers, i.e. films and three-dimensional systems) the exact result and the asymptotic one are graphically presented and compared on the basis of the calculated relative errors. The obtained result holds true in a broader neighborhood of the critical point. The expansion of the critical region is estimated at the three real physical dimensionalities.

Research paper thumbnail of A Theorem for Local Convergence of Halley’s Method for Finding Polynomial Zeros Simultaneously

In this note we present a local convergence theorem of Halley's iterative method considered a... more In this note we present a local convergence theorem of Halley's iterative method considered as a method for finding all zeros of a polynomial simultaneously. The main result is based on a new local convergence theory for iterative processes published in 2009 by the first author.

Research paper thumbnail of On the Critical Behavior of the Inverse Susceptibility of a Model of Structural Phase Transitions

An exactly solvable lattice model describing structural phase transitions in an anharmonic crysta... more An exactly solvable lattice model describing structural phase transitions in an anharmonic crystal with long-range interaction is considered in the neighborhoods of the quantum and classical critical points at the corresponding upper critical dimensions. In a broader neighborhood of the critical region the inverse susceptibility of the model is exactly calculated in terms of the Lambert W-function and graphically presented as a function of the deviation from the critical point and the upper critical dimension. For quantum and classical systems with real physical dimensions (chains, thin layers and three-dimensional systems) the exact results are compared with the asymptotic ones on the basis of some numerical data for their ratio. Relative errors are also provided.

Research paper thumbnail of On the Convergence of Halley’s Method for Multiple Polynomial Zeros

Mediterranean Journal of Mathematics, 2014

In this paper, we investigate the local convergence of Halley's method for the computation of a m... more In this paper, we investigate the local convergence of Halley's method for the computation of a multiple polynomial zero with known multiplicity. We establish two local convergence theorems for Halley's method for multiple polynomial zeros under different initial conditions. The convergence of these results is cubic right from the first iteration. Also we find an initial condition which guarantees that an initial guess is an approximate zero of the second kind for Halley's method. All of the results are new even in the case of simple zeros.