The Experts below are selected from a list of 1395 Experts worldwide ranked by ideXlab platform

Alexander Shlemov - One of the best experts on this subject based on the ideXlab platform.

  • Variations of Singular Spectrum Analysis for separability improvement: non-orthogonal decompositions of time series
    2016
    Co-Authors: Nina Goly, Alexander Shlemov
    Abstract:

    Singular spectrum analysis (SSA) as a nonparametric tool for decompo-sition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by SSA means the possibility of such decomposition. Two vari-ations of SSA, which weaken the separability conditions, are proposed. Both proposed approaches consider Inner Products corresponding to oblique coor-dinate systems instead of the conventional Euclidean Inner Product. One of the approaches performs iterations to obtain separating Inner Products. The other method changes contributions of the components by involving the series derivative to avoid component mixing. Performance of the suggested methods is demonstrated on simulated and real-life data. Keywords: Singular Spec-trum Analysis, time series, time series analysis, time series decomposition, separabilit

  • variations of singular spectrum analysis for separability improvement non orthogonal decompositions of time series
    Statistics and Its Interface, 2015
    Co-Authors: Nina Golyandina, Alexander Shlemov
    Abstract:

    Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by SSA means the possibility of such decomposition. Two extensions of SSA, which weaken the separability conditions, are proposed. One of the proposed approaches considers Inner Products corresponding to oblique coordinate systems instead of the conventional Euclidean Inner Product. The other method changes contributions of the components by involving the series derivative to avoid component mixing. Performance of the suggested methods is demonstrated on simulated and real-life data.

  • variations of singular spectrum analysis for separability improvement non orthogonal decompositions of time series
    arXiv: Methodology, 2013
    Co-Authors: Nina Golyandina, Alexander Shlemov
    Abstract:

    Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by SSA means the possibility of such decomposition. Two variations of SSA, which weaken the separability conditions, are proposed. Both proposed approaches consider Inner Products corresponding to oblique coordinate systems instead of the conventional Euclidean Inner Product. One of the approaches performs iterations to obtain separating Inner Products. The other method changes contributions of the components by involving the series derivative to avoid component mixing. Performance of the suggested methods is demonstrated on simulated and real-life data.

Michiel E Hochstenbach - One of the best experts on this subject based on the ideXlab platform.

  • a jacobi davidson method for solving complex symmetric eigenvalue problems
    SIAM Journal on Scientific Computing, 2004
    Co-Authors: Peter Arbenz, Michiel E Hochstenbach
    Abstract:

    We discuss variants of the Jacobi--Davidson method for solving the generalized complex symmetric eigenvalue problem. The Jacobi--Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean Inner Product in ${\mathbb C}^n$ with an indefinite Inner Product. The Rayleigh quotient based on this indefinite Inner Product leads to an asymptotically cubically convergent Rayleigh quotient iteration. Advantages of the method are illustrated by numerical examples. We deal with problems from electromagnetics that require the computation of interior eigenvalues. The main drawback that we experience in these particular examples is the lack of efficient preconditioners.

  • a jacobi davidson method for solving complex symmetric eigenvalue problems
    Technical report ETH Zürich Department of Computer Science, 2002
    Co-Authors: Peter Arbenz, Michiel E Hochstenbach
    Abstract:

    We discuss variants of the Jacobi–Davidson method for solving the generalized complex-symmetric eigenvalue problem. The Jacobi–Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean Inner Product xy in Cn by the bilinear form xT y. The Rayleigh quotient based on this bilinear form leads to an asymptotically cubically convergent Rayleigh quotient iteration. Advantages of the method are illustrated by numerical examples. We deal with problems from electromagnetics that require the computation of interior eigenvalues.

Nina Golyandina - One of the best experts on this subject based on the ideXlab platform.

  • variations of singular spectrum analysis for separability improvement non orthogonal decompositions of time series
    Statistics and Its Interface, 2015
    Co-Authors: Nina Golyandina, Alexander Shlemov
    Abstract:

    Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by SSA means the possibility of such decomposition. Two extensions of SSA, which weaken the separability conditions, are proposed. One of the proposed approaches considers Inner Products corresponding to oblique coordinate systems instead of the conventional Euclidean Inner Product. The other method changes contributions of the components by involving the series derivative to avoid component mixing. Performance of the suggested methods is demonstrated on simulated and real-life data.

  • variations of singular spectrum analysis for separability improvement non orthogonal decompositions of time series
    arXiv: Methodology, 2013
    Co-Authors: Nina Golyandina, Alexander Shlemov
    Abstract:

    Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by SSA means the possibility of such decomposition. Two variations of SSA, which weaken the separability conditions, are proposed. Both proposed approaches consider Inner Products corresponding to oblique coordinate systems instead of the conventional Euclidean Inner Product. One of the approaches performs iterations to obtain separating Inner Products. The other method changes contributions of the components by involving the series derivative to avoid component mixing. Performance of the suggested methods is demonstrated on simulated and real-life data.

Pierre-philippe Dechant - One of the best experts on this subject based on the ideXlab platform.

  • Clifford Algebra is the Natural Framework for Root Systems and Coxeter Groups. Group Theory: Coxeter, Conformal and Modular Groups
    Advances in Applied Clifford Algebras, 2017
    Co-Authors: Pierre-philippe Dechant
    Abstract:

    In this paper, we make the case that Clifford algebra is the natural framework for root systems and reflection groups, as well as related groups such as the conformal and modular groups: The metric that exists on these spaces can always be used to construct the corresponding Clifford algebra. Via the Cartan–Dieudonné theorem all the transformations of interest can be written as Products of reflections and thus via ‘sandwiching’ with Clifford algebra multivectors. These multivector groups can be used to perform concrete calculations in different groups, e.g. the various types of polyhedral groups, and we treat the example of the tetrahedral group A _3 in detail. As an aside, this gives a constructive result that induces from every 3D root system a root system in dimension four, which hinges on the facts that the group of spinors provides a double cover of the rotations, the space of 3D spinors has a 4D Euclidean Inner Product, and with respect to this Inner Product the group of spinors can be shown to be closed under reflections. In particular the 4D root systems/Coxeter groups induced in this way are precisely the exceptional ones, with the 3D spinorial point of view also explaining their unusual automorphism groups. This construction simplifies Arnold’s trinities and puts the McKay correspondence into a wider framework. We finally discuss extending the conformal geometric algebra approach to the 2D conformal and modular groups, which could have interesting novel applications in conformal field theory, string theory and modular form theory.

  • clifford algebra is the natural framework for root systems and coxeter groups group theory coxeter conformal and modular groups
    Advances in Applied Clifford Algebras, 2017
    Co-Authors: Pierre-philippe Dechant
    Abstract:

    In this paper, we make the case that Clifford algebra is the natural framework for root systems and reflection groups, as well as related groups such as the conformal and modular groups: The metric that exists on these spaces can always be used to construct the corresponding Clifford algebra. Via the Cartan–Dieudonne theorem all the transformations of interest can be written as Products of reflections and thus via ‘sandwiching’ with Clifford algebra multivectors. These multivector groups can be used to perform concrete calculations in different groups, e.g. the various types of polyhedral groups, and we treat the example of the tetrahedral group A 3 in detail. As an aside, this gives a constructive result that induces from every 3D root system a root system in dimension four, which hinges on the facts that the group of spinors provides a double cover of the rotations, the space of 3D spinors has a 4D Euclidean Inner Product, and with respect to this Inner Product the group of spinors can be shown to be closed under reflections. In particular the 4D root systems/Coxeter groups induced in this way are precisely the exceptional ones, with the 3D spinorial point of view also explaining their unusual automorphism groups. This construction simplifies Arnold’s trinities and puts the McKay correspondence into a wider framework. We finally discuss extending the conformal geometric algebra approach to the 2D conformal and modular groups, which could have interesting novel applications in conformal field theory, string theory and modular form theory.

Peter Arbenz - One of the best experts on this subject based on the ideXlab platform.

  • a jacobi davidson method for solving complex symmetric eigenvalue problems
    SIAM Journal on Scientific Computing, 2004
    Co-Authors: Peter Arbenz, Michiel E Hochstenbach
    Abstract:

    We discuss variants of the Jacobi--Davidson method for solving the generalized complex symmetric eigenvalue problem. The Jacobi--Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean Inner Product in ${\mathbb C}^n$ with an indefinite Inner Product. The Rayleigh quotient based on this indefinite Inner Product leads to an asymptotically cubically convergent Rayleigh quotient iteration. Advantages of the method are illustrated by numerical examples. We deal with problems from electromagnetics that require the computation of interior eigenvalues. The main drawback that we experience in these particular examples is the lack of efficient preconditioners.

  • a jacobi davidson method for solving complex symmetric eigenvalue problems
    Technical report ETH Zürich Department of Computer Science, 2002
    Co-Authors: Peter Arbenz, Michiel E Hochstenbach
    Abstract:

    We discuss variants of the Jacobi–Davidson method for solving the generalized complex-symmetric eigenvalue problem. The Jacobi–Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean Inner Product xy in Cn by the bilinear form xT y. The Rayleigh quotient based on this bilinear form leads to an asymptotically cubically convergent Rayleigh quotient iteration. Advantages of the method are illustrated by numerical examples. We deal with problems from electromagnetics that require the computation of interior eigenvalues.