The Experts below are selected from a list of 23826 Experts worldwide ranked by ideXlab platform
Mattias Nyberg - One of the best experts on this subject based on the ideXlab platform.
-
brief a Minimal Polynomial basis solution to residual generation for fault diagnosis in linear systems
Automatica, 2001Co-Authors: Erik Frisk, Mattias NybergAbstract:A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the Minimal Polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding Polynomial bases for null-spaces of Polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the Minimal Polynomial basis approach can find all possible residual generators and explicitly those of Minimal order.
-
a Minimal Polynomial basis solution to residual generation for fault diagnosis in linear systems
IFAC Proceedings Volumes, 1999Co-Authors: Mattias Nyberg, Erik FriskAbstract:Abstract A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the Minimal Polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding Polynomial bases for null-spaces of Polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the Minimal Polynomial basis approach can find all possible residual generators, including those of Minimal McMillan degree, and the solution has a Minimal parameterization. It is shown that some other well known design methods, do not have these properties.
-
Using Minimal Polynomial bases for fault diagnosis
1999 European Control Conference (ECC), 1999Co-Authors: Erik Frisk, Mattias NybergAbstract:A fundamental part of a fault diagnosis system is the residual generator. Design of residual generators to achieve perfect decoupling in linear systems is considered. A new method, the Minimal Polynomial basis approach, is presented, where the residual generation problem is transformed into the problem of finding Polynomial bases for null-spaces of Polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the Minimal Polynomial basis approach can find all possible residual generators, including those of Minimal degree, and the solution has a Minimal parameterization.
Erik Frisk - One of the best experts on this subject based on the ideXlab platform.
-
brief a Minimal Polynomial basis solution to residual generation for fault diagnosis in linear systems
Automatica, 2001Co-Authors: Erik Frisk, Mattias NybergAbstract:A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the Minimal Polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding Polynomial bases for null-spaces of Polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the Minimal Polynomial basis approach can find all possible residual generators and explicitly those of Minimal order.
-
a Minimal Polynomial basis solution to residual generation for fault diagnosis in linear systems
IFAC Proceedings Volumes, 1999Co-Authors: Mattias Nyberg, Erik FriskAbstract:Abstract A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the Minimal Polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding Polynomial bases for null-spaces of Polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the Minimal Polynomial basis approach can find all possible residual generators, including those of Minimal McMillan degree, and the solution has a Minimal parameterization. It is shown that some other well known design methods, do not have these properties.
-
Using Minimal Polynomial bases for fault diagnosis
1999 European Control Conference (ECC), 1999Co-Authors: Erik Frisk, Mattias NybergAbstract:A fundamental part of a fault diagnosis system is the residual generator. Design of residual generators to achieve perfect decoupling in linear systems is considered. A new method, the Minimal Polynomial basis approach, is presented, where the residual generation problem is transformed into the problem of finding Polynomial bases for null-spaces of Polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the Minimal Polynomial basis approach can find all possible residual generators, including those of Minimal degree, and the solution has a Minimal parameterization.
Denis Vasilyev - One of the best experts on this subject based on the ideXlab platform.
-
counting real algebraic numbers with bounded derivative of Minimal Polynomial
International Journal of Number Theory, 2019Co-Authors: Alexey Kudin, Denis VasilyevAbstract:In this paper, we consider the problem of counting algebraic numbers α of fixed degree n and bounded height Q such that the derivative of the Minimal Polynomial Pα(x) of α is bounded, Pα′(α) < Q1−v...
-
counting real algebraic numbers with bounded derivative of Minimal Polynomial
arXiv: Number Theory, 2018Co-Authors: Alexey Kudin, Denis VasilyevAbstract:In this paper we consider the problem of counting algebraic numbers $\alpha$ of fixed degree $n$ and bounded height $Q$ such that the derivative of the Minimal Polynomial $P_{\alpha}(x)$ of $\alpha$ is bounded, $|P_{\alpha}'(\alpha)| Q_0(n)$ and $1.4 \le v \le \frac{7}{16}(n+1)$. Our result is based on an improvement to the lemma on the order of zero approximation by irreducible divisors of integer Polynomials from A. Gelfond's monograph "Transcendental and algebraic numbers". The improvement provides a stronger estimate for the absolute value of the divisor in real points which are located far enough from all algebraic numbers of bounded degree and height and it's based on the representation of the resultant of two Polynomials as the determinant of Sylvester matrix for the shifted Polynomials. Keywords: Diophantine approximation, Hausdorff dimension, transcendental numbers, resultant, Sylvester matrix, irreducible divisor, Gelfond's lemma.
P. Koulmann - One of the best experts on this subject based on the ideXlab platform.
-
Minimal dimension of symmetric or skew-symmetric matrices of given Minimal Polynomial
Journal of Pure and Applied Algebra, 2001Co-Authors: P. KoulmannAbstract:Over a field k of characteristic not 2 the set of Minimal Polynomials of symmetric or skew-symmetric matrices (with respect to an involution of the first kind) is known. We give the smallest possible dimension of a symmetric or skew-symmetric matrix of given Minimal Polynomial depending on the type of the involution. Concerning the transpose, we give the smallest constant c such that any suitable Polynomial f is the Minimal Polynomial of a symmetric (resp. skew-symmetric) matrix of dimension c deg f. The case of Polynomials of degree 2 is completely solved. (C) 2001 Elsevier Science B.V. All rights reserved.
-
Minimal dimension of symmetric or skew-symmetric matrices of given Minimal Polynomial
Journal of Pure and Applied Algebra, 2001Co-Authors: P. KoulmannAbstract:AbstractOver a field k of characteristic not 2 the set of Minimal Polynomials of symmetric or skew-symmetric matrices (with respect to an involution of the first kind) is known. We give the smallest possible dimension of a symmetric or skew-symmetric matrix of given Minimal Polynomial depending on the type of the involution. Concerning the transpose, we give the smallest constant c such that any suitable Polynomial f is the Minimal Polynomial of a symmetric (resp. skew-symmetric) matrix of dimension cdegf. The case of Polynomials of degree 2 is completely solved
Avram Sidi - One of the best experts on this subject based on the ideXlab platform.
-
Minimal Polynomial and reduced rank extrapolation methods are related
Advances in Computational Mathematics, 2017Co-Authors: Avram SidiAbstract:Minimal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are two Polynomial methods used for accelerating the convergence of sequences of vectors {xm}. They are applied successfully in conjunction with fixed-point iterative schemes in the solution of large and sparse systems of linear and nonlinear equations in different disciplines of science and engineering. Both methods produce approximations sk to the limit or antilimit of {xm} that are of the form sk=źi=0kźixi$\boldsymbol {s}_{k}={\sum }^{k}_{i=0}\gamma _{i}\boldsymbol {x}_{i}$ with źi=0kźi=1${\sum }^{k}_{i=0}\gamma _{i}=1$, for some scalars źi. The way the two methods are derived suggests that they might, somehow, be related to each other; this has not been explored so far, however. In this work, we tackle this issue and show that the vectors skMPE$\boldsymbol {s}_{k}^{\textit {{\tiny {MPE}}}}$ and skRRE$\boldsymbol {s}_{k}^{\textit {{\tiny {RRE}}}}$ produced by the two methods are related in more than one way, and independently of the way the xm are generated. One of our results states that RRE stagnates, in the sense that skRRE=skź1RRE$\boldsymbol {s}_{k}^{\textit {{\tiny {RRE}}}}=\boldsymbol {s}_{k-1}^{\textit {{\tiny {RRE}}}}$, if and only if skMPE$\boldsymbol {s}_{k}^{\textit {{\tiny {MPE}}}}$ does not exist. Another result states that, when skMPE$\boldsymbol {s}_{k}^{\textit {{\tiny {MPE}}}}$ exists, there holds μkskRRE=μkź1skź1RRE+źkskMPEwithμk=μkź1+źk,$$\mu_{k}\boldsymbol{s}_{k}^{\textit{{\tiny{RRE}}}}=\mu_{k-1}\boldsymbol{s}_{k-1}^{\textit{{\tiny{RRE}}}}+ \nu_{k}\boldsymbol{s}_{k}^{\textit{{\tiny{MPE}}}}\quad \text{with}\quad \mu_{k}=\mu_{k-1}+\nu_{k}, $$for some positive scalars μk, μkź1, and źk that depend only on skRRE$\boldsymbol {s}_{k}^{\textit {{\tiny {RRE}}}}$, skź1RRE$\boldsymbol {s}_{k-1}^{\textit {{\tiny {RRE}}}}$, and skMPE$\boldsymbol {s}_{k}^{\textit {{\tiny {MPE}}}}$, respectively. Our results are valid when MPE and RRE are defined in any weighted inner product and the norm induced by it. They also contain as special cases the known results pertaining to the connection between the method of Arnoldi and the method of generalized Minimal residuals, two important Krylov subspace methods for solving nonsingular linear systems.
-
Minimal Polynomial and reduced rank extrapolation methods are related
arXiv: Numerical Analysis, 2015Co-Authors: Avram SidiAbstract:Minimal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are two Polynomial methods used for accelerating the convergence of sequences of vectors $\{{x}_m\}$. They are applied successfully in conjunction with fixed-point iterative schemes in the solution of large and sparse systems of linear and nonlinear equations in different disciplines of science and engineering. Both methods produce approximations $s_k$ to the limit or antilimit of $\{{x}_m\}$ that are of the form ${s}_k=\sum^k_{i=0}\gamma_i{x}_i$ with $\sum^k_{i=0}\gamma_i=1$, for some scalars $\gamma_i$. The way the two methods are derived suggests that they might, somehow, be related to each other; this has not been explored so far, however. In this work, we tackle this issue and show that the vectors $s_{k}^\text{MPE}$ and $s_k^\text{RRE}$ produced by the two methods are related in more than one way, and independently of the way the $x_m$ are generated. One of our results states that RRE stagnates, in the sense that ${s}_k^\text{RRE}={s}_{k-1}^\text{RRE}$, if and only if ${s}_{k}^\text{MPE}$ does not exist. Another result states that, when ${s}_{k}^\text{MPE}$ exists, there holds $$\mu_k{s}_k^\text{RRE} = \mu_{k-1}{s}_{k-1}^\text{RRE} + \nu_k{s}_{k}^\text{MPE} \quad \text{with} \quad \mu_k = \mu_{k-1} + \nu_k,$$ for some positive scalars $\mu_k$, $\mu_{k-1}$, and $\nu_k$ that depend only on ${s}_k^\text{RRE}$, ${s}_{k-1}^\text{RRE}$, and ${s}_{k}^\text{MPE}$, respectively. Our results are valid when MPE and RRE are defined in any weighted inner product and the norm induced by it. They also contain as special cases the known results pertaining to the connection between the method of Arnoldi and the method of generalized Minimal residuals, two important Krylov subspace methods for solving nonsingular linear systems.
-
efficient implementation of Minimal Polynomial and reduced rank extrapolation methods
Journal of Computational and Applied Mathematics, 1991Co-Authors: Avram SidiAbstract:Abstract The Minimal Polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two very effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equations. Their definitions involve some linear least-squares problems, and this causes difficulties in their numerical implementation. In this work timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems, among them a hypersonic flow problem involving chemical reactions.