Rogério Serôdio | Universidade da Beira Interior (original) (raw)
Papers by Rogério Serôdio
Mathematical methods in the applied sciences, Jun 11, 2024
Mathematical methods in the applied sciences, May 20, 2024
Authorea (Authorea), Sep 29, 2023
Computers & mathematics with applications, Oct 1, 2001
A method is developed to compute the zeros of a quaternion polynomial with all terms of the form ... more A method is developed to compute the zeros of a quaternion polynomial with all terms of the form ok Xk. This method is based essentially in Niven's algorithm (11, which consists of dividing the polynomial by a characteristic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the companion matrix associated to the polynomial. The companion matrix is represented by a matrix with complex entries. Three numerical examples using Mathematics 2.2 version are given.
mat.uc.pt
Abstract: The aim of this paper is to propose an iterative method to compute the dominant zero of... more Abstract: The aim of this paper is to propose an iterative method to compute the dominant zero of a quaternion polynomial. We prove that the method is convergent in the sense that it generates a sequence of quaternions that converges to the dominant zero of the ...
Ars Mathematica Contemporanea, Feb 28, 2019
In this paper, we describe subspaces of generalized Hessenberg matrices where the determinant is ... more In this paper, we describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. These subspaces can arise from different numberings of the vertices of a graph. With this numbering process, we obtain some well-known sequences of integers. For instance, in the case of a path of length n, we prove that the number of these subspaces is the (n + 1) th Fibonacci number.
Motricidade, Dec 19, 2018
The study explores the technical optimization of an athlete through the use of intelligent system... more The study explores the technical optimization of an athlete through the use of intelligent system performance metrics that produce information obtained from inertial sensors associated to the coach's technical qualifications in real time, using Mixed Methods and Machine Learning. The purpose of this study is to illustrate, from the confusion matrices, the different performance metrics that provide information of high pertinence for the sports training in context. 2000 technical fencing actions with two levels of complexity were performed, captured through a single sensor applied in the armed hand and, simultaneously, the gesture's qualification through a dichotomous way by the coach. The signals were divided into segments through Dynamic Time Warping, with the resulting extracted characteristics and qualitative assessments being fed to a Neural Network to learn the patterns inherent to a good or poor execution. The performance analysis of the resulting models returned a prediction accuracy of 76.6% and 72.7% for each exercise, but other metrics indicate the existence of high bias in the data. The study demonstrates the potential of intelligent algorithms to uncover trends not captured by other statistical methods.
Advances in Applied Clifford Algebras, Jun 16, 2017
This is a work on an application of the real split-quaternions to Spatial Analytic Geometry. Conc... more This is a work on an application of the real split-quaternions to Spatial Analytic Geometry. Concretely, the intersection of a double cone and a line, which can be the empty set, a point, two points or a line, is studied in the real split-quaternions setting.
Advances in Applied Clifford Algebras, Feb 16, 2007
Abstract. We discuss the generalization of results on quaternionic polynomials to the octonionic ... more Abstract. We discuss the generalization of results on quaternionic polynomials to the octonionic polynomials. In contrast to the quaternions the octonionic multiplication is non-associative. This fact although introducing some difficulties nevertheless leads to some ...
Computer Physics Communications, Feb 1, 2023
EDULEARN proceedings, Jul 1, 2020
Computers & mathematics with applications, Oct 1, 2005
The objective of the present work is to study the solution of quaternion block quasitridiagonal s... more The objective of the present work is to study the solution of quaternion block quasitridiagonal systems. Kershaw and Rdzsa and Romani have proposed a method for calculating matrix inverses using second kind Chebyshev polynomials. This method has been generalized later to block tridiagonal matrices with quaternionic entries by Costa and Ser6dio. In the present work, we make use of this method to solve block quasi-tridiagonal systems of the same kind. The computational effort to obtain the solution is evaluated, and future more efficient strategies are proposed. (~ 2005 Elsevier Ltd. All rights reserved. Keywords-Block tridiagonal matrices, Block quasi-tridiagonal matrices, Chebyshev polynomials, Quaternions.
Physical review, Apr 29, 2009
We analyze the quantum description of a free scalar field on the circle in the presence of an exp... more We analyze the quantum description of a free scalar field on the circle in the presence of an explicitly time dependent potential, also interpretable as a time dependent mass. Classically, the field satisfies a linear wave equation of the formξ − ξ ′′ + f (t)ξ = 0. We prove that the representation of the canonical commutation relations corresponding to the particular case of a massless free field (f = 0) provides a unitary implementation of the dynamics for sufficiently general mass terms, f (t). Furthermore, this representation is uniquely specified, among the class of representations determined by S 1-invariant complex structures, as the only one allowing a unitary dynamics. These conclusions can be extended in fact to fields on the two-sphere possessing axial symmetry. This generalizes a uniqueness result previously obtained in the context of the quantum field description of the Gowdy cosmologies, in the case of linear polarization and for any of the possible topologies of the spatial sections.
Advances in Applied Clifford Algebras, Nov 5, 2008
Abstract. In a previous paper [On Octonionic Polynomials, Advances in Applied Clifford Algebras... more Abstract. In a previous paper [On Octonionic Polynomials, Advances in Applied Clifford Algebras, 17 (2),(2007), 245258] we discussed generalizations of results on quaternionic polynomials to the octonionic polynomials. In this paper, we continue this generalization ...
The aim of this paper is to propose an iterative method to compute the dominant zero of a quatern... more The aim of this paper is to propose an iterative method to compute the dominant zero of a quaternion polynomial. We prove that the method is convergent in the sense that it generates a sequence of quaternions that converges to the dominant zero of the polynomial. The idea subjacent to the proposed method is the well known method proposed by Sebastião e Silva in "Sur une méthode d'approximation semblable à celle de Gräffe", Portugaliae Mathematica, 1941, to compute approximately the zeros of complex polynomials.
Analele Stiintifice Ale Universitatii Ovidius Constanta-seria Matematica, Nov 1, 2021
In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to t... more In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials.
Advances in Applied Clifford Algebras, Apr 26, 2018
The aim of this paper is to propose an iterative method to compute the dominant zero of a quatern... more The aim of this paper is to propose an iterative method to compute the dominant zero of a quaternionic unilateral polynomial. We prove that the method is convergent in the sense that it generates a sequence of quaternions that converges to the dominant zero of the polynomial. The idea subjacent to this method is the well known Sebastião e Silva's method, proposed in "Sur une méthode d'approximation semblableà celle de Gräffe", Portugaliae Mathematica, 1941, to approximate the dominant zero of complex polynomials.
Computers & Mathematics with Applications, 2005
The objective of the present work is to study the solution of quaternion block quasitridiagonal s... more The objective of the present work is to study the solution of quaternion block quasitridiagonal systems. Kershaw and Rdzsa and Romani have proposed a method for calculating matrix inverses using second kind Chebyshev polynomials. This method has been generalized later to block tridiagonal matrices with quaternionic entries by Costa and Ser6dio. In the present work, we make use of this method to solve block quasi-tridiagonal systems of the same kind. The computational effort to obtain the solution is evaluated, and future more efficient strategies are proposed. (~ 2005 Elsevier Ltd. All rights reserved. Keywords-Block tridiagonal matrices, Block quasi-tridiagonal matrices, Chebyshev polynomials, Quaternions.
Mathematical methods in the applied sciences, Jun 11, 2024
Mathematical methods in the applied sciences, May 20, 2024
Authorea (Authorea), Sep 29, 2023
Computers & mathematics with applications, Oct 1, 2001
A method is developed to compute the zeros of a quaternion polynomial with all terms of the form ... more A method is developed to compute the zeros of a quaternion polynomial with all terms of the form ok Xk. This method is based essentially in Niven's algorithm (11, which consists of dividing the polynomial by a characteristic polynomial associated to a zero. The information about the trace and the norm of the zero is obtained by an original idea which requires the companion matrix associated to the polynomial. The companion matrix is represented by a matrix with complex entries. Three numerical examples using Mathematics 2.2 version are given.
mat.uc.pt
Abstract: The aim of this paper is to propose an iterative method to compute the dominant zero of... more Abstract: The aim of this paper is to propose an iterative method to compute the dominant zero of a quaternion polynomial. We prove that the method is convergent in the sense that it generates a sequence of quaternions that converges to the dominant zero of the ...
Ars Mathematica Contemporanea, Feb 28, 2019
In this paper, we describe subspaces of generalized Hessenberg matrices where the determinant is ... more In this paper, we describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. These subspaces can arise from different numberings of the vertices of a graph. With this numbering process, we obtain some well-known sequences of integers. For instance, in the case of a path of length n, we prove that the number of these subspaces is the (n + 1) th Fibonacci number.
Motricidade, Dec 19, 2018
The study explores the technical optimization of an athlete through the use of intelligent system... more The study explores the technical optimization of an athlete through the use of intelligent system performance metrics that produce information obtained from inertial sensors associated to the coach's technical qualifications in real time, using Mixed Methods and Machine Learning. The purpose of this study is to illustrate, from the confusion matrices, the different performance metrics that provide information of high pertinence for the sports training in context. 2000 technical fencing actions with two levels of complexity were performed, captured through a single sensor applied in the armed hand and, simultaneously, the gesture's qualification through a dichotomous way by the coach. The signals were divided into segments through Dynamic Time Warping, with the resulting extracted characteristics and qualitative assessments being fed to a Neural Network to learn the patterns inherent to a good or poor execution. The performance analysis of the resulting models returned a prediction accuracy of 76.6% and 72.7% for each exercise, but other metrics indicate the existence of high bias in the data. The study demonstrates the potential of intelligent algorithms to uncover trends not captured by other statistical methods.
Advances in Applied Clifford Algebras, Jun 16, 2017
This is a work on an application of the real split-quaternions to Spatial Analytic Geometry. Conc... more This is a work on an application of the real split-quaternions to Spatial Analytic Geometry. Concretely, the intersection of a double cone and a line, which can be the empty set, a point, two points or a line, is studied in the real split-quaternions setting.
Advances in Applied Clifford Algebras, Feb 16, 2007
Abstract. We discuss the generalization of results on quaternionic polynomials to the octonionic ... more Abstract. We discuss the generalization of results on quaternionic polynomials to the octonionic polynomials. In contrast to the quaternions the octonionic multiplication is non-associative. This fact although introducing some difficulties nevertheless leads to some ...
Computer Physics Communications, Feb 1, 2023
EDULEARN proceedings, Jul 1, 2020
Computers & mathematics with applications, Oct 1, 2005
The objective of the present work is to study the solution of quaternion block quasitridiagonal s... more The objective of the present work is to study the solution of quaternion block quasitridiagonal systems. Kershaw and Rdzsa and Romani have proposed a method for calculating matrix inverses using second kind Chebyshev polynomials. This method has been generalized later to block tridiagonal matrices with quaternionic entries by Costa and Ser6dio. In the present work, we make use of this method to solve block quasi-tridiagonal systems of the same kind. The computational effort to obtain the solution is evaluated, and future more efficient strategies are proposed. (~ 2005 Elsevier Ltd. All rights reserved. Keywords-Block tridiagonal matrices, Block quasi-tridiagonal matrices, Chebyshev polynomials, Quaternions.
Physical review, Apr 29, 2009
We analyze the quantum description of a free scalar field on the circle in the presence of an exp... more We analyze the quantum description of a free scalar field on the circle in the presence of an explicitly time dependent potential, also interpretable as a time dependent mass. Classically, the field satisfies a linear wave equation of the formξ − ξ ′′ + f (t)ξ = 0. We prove that the representation of the canonical commutation relations corresponding to the particular case of a massless free field (f = 0) provides a unitary implementation of the dynamics for sufficiently general mass terms, f (t). Furthermore, this representation is uniquely specified, among the class of representations determined by S 1-invariant complex structures, as the only one allowing a unitary dynamics. These conclusions can be extended in fact to fields on the two-sphere possessing axial symmetry. This generalizes a uniqueness result previously obtained in the context of the quantum field description of the Gowdy cosmologies, in the case of linear polarization and for any of the possible topologies of the spatial sections.
Advances in Applied Clifford Algebras, Nov 5, 2008
Abstract. In a previous paper [On Octonionic Polynomials, Advances in Applied Clifford Algebras... more Abstract. In a previous paper [On Octonionic Polynomials, Advances in Applied Clifford Algebras, 17 (2),(2007), 245258] we discussed generalizations of results on quaternionic polynomials to the octonionic polynomials. In this paper, we continue this generalization ...
The aim of this paper is to propose an iterative method to compute the dominant zero of a quatern... more The aim of this paper is to propose an iterative method to compute the dominant zero of a quaternion polynomial. We prove that the method is convergent in the sense that it generates a sequence of quaternions that converges to the dominant zero of the polynomial. The idea subjacent to the proposed method is the well known method proposed by Sebastião e Silva in "Sur une méthode d'approximation semblable à celle de Gräffe", Portugaliae Mathematica, 1941, to compute approximately the zeros of complex polynomials.
Analele Stiintifice Ale Universitatii Ovidius Constanta-seria Matematica, Nov 1, 2021
In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to t... more In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials.
Advances in Applied Clifford Algebras, Apr 26, 2018
The aim of this paper is to propose an iterative method to compute the dominant zero of a quatern... more The aim of this paper is to propose an iterative method to compute the dominant zero of a quaternionic unilateral polynomial. We prove that the method is convergent in the sense that it generates a sequence of quaternions that converges to the dominant zero of the polynomial. The idea subjacent to this method is the well known Sebastião e Silva's method, proposed in "Sur une méthode d'approximation semblableà celle de Gräffe", Portugaliae Mathematica, 1941, to approximate the dominant zero of complex polynomials.
Computers & Mathematics with Applications, 2005
The objective of the present work is to study the solution of quaternion block quasitridiagonal s... more The objective of the present work is to study the solution of quaternion block quasitridiagonal systems. Kershaw and Rdzsa and Romani have proposed a method for calculating matrix inverses using second kind Chebyshev polynomials. This method has been generalized later to block tridiagonal matrices with quaternionic entries by Costa and Ser6dio. In the present work, we make use of this method to solve block quasi-tridiagonal systems of the same kind. The computational effort to obtain the solution is evaluated, and future more efficient strategies are proposed. (~ 2005 Elsevier Ltd. All rights reserved. Keywords-Block tridiagonal matrices, Block quasi-tridiagonal matrices, Chebyshev polynomials, Quaternions.