1,721,026 research outputs found
Numerical Linear Algebra and the Applications
No full textNumerical linear algebra is a very important topic in mathematics and has important recent applications in deep learning, machine learning, image processing, applied statistics, artificial intelligence and other interesting modern applications in many fields. The purpose of this Special Issue in Mathematics is to present the latest contributions and recent developments in numerical linear algebra and applications in different real domains. We invite authors to submit original and new papers and high-quality reviews related to the following topics: applied linear algebra, linear and nonlinear systems of equations, large matrix equations, numerical tensor problems with applications, ill-posed problems and image processing, linear algebra and applied statistics, model reduction in dynamic systems, and other related subjects. The submitted papers will be reviewed in line with the traditional submission process. This Special Issue will be dedicated to the inspired mathematician Constantin Petridi, who has devoted his life to mathematics
Numerical Linear Algebra and the Applications
Full text linkNumerical linear algebra is a very important topic in mathematics and has important recent applications in deep learning, machine learning, image processing, applied statistics, artificial intelligence and other interesting modern applications in many fields. The purpose of this Special Issue in Mathematics is to present the latest contributions and recent developments in numerical linear algebra and applications in different real domains. We invite authors to submit original and new papers and high-quality reviews related to the following topics: applied linear algebra, linear and nonlinear systems of equations, large matrix equations, numerical tensor problems with applications, ill-posed problems and image processing, linear algebra and applied statistics, model reduction in dynamic systems, and other related subjects. The submitted papers will be reviewed in line with the traditional submission process. This Special Issue will be dedicated to the inspired mathematician Constantin Petridi, who has devoted his life to mathematics
A rational Krylov methods for large scale linear multidimensional dynamical systems
No full textIn this paper, we investigate the use of multilinear algebra for reducing the order of multidimensional linear time-invariant (MLTI) systems. Our main tools are tensor rational Krylov subspace methods, which enable us to approximate the systems solution within a low-dimensional subspace. We introduce the tensor rational block Arnoldi and tensor rational block Lanczos algorithms. By utilizing these methods, we develop a model reduction approach based on projection techniques. Additionally, we demonstrate how these approaches can be applied to large-scale Lyapunov tensor equations, which are critical for the balanced truncation method, a well-known technique for order reduction. An adaptive method for choosing the interpolation points is also introduced. Finally, some numerical experiments are reported to show the effectiveness of the proposed adaptive approaches.arXiv admin note: text overlap with arXiv:2305.0936
A Tangential Block Lanczos Method for Model Reduction of Large-Scale First and Second Order Dynamical Systems
No full textInternational audienceIn this paper, we present a new approach for model reduction of large scale first and second order dynamical systems with multiple inputs and multiple outputs. This approach is based on the projection of the initial problem onto tangential subspaces to produce a simpler reduced-order model that approximates well the behaviour of the original model. We present an algorithm named: adaptive block tangential Lanczos-type algorithm. We give some algebraic properties and present some numerical experiences to show the effectiveness of the proposed algorithms
Numerical methods for differential linear matrix equations via Krylov subspace methods
No full textInternational audienceIn the present paper, we present some numerical methods for computing approximate solutions to some large differential linear matrix equations. In the first part of this work, we deal with differential generalized Sylvester matrix equations with full rank right-hand sides using a global Galerkin and a norm-minimization approaches. In the second part, we consider large differential Lyapunov matrix equations with low rank right-hand sides and use the extended global Arnoldi process to produce low rank approximate solutions. We give some theoretical results and present some numerical examples
Projection-minimization methods for nonsymmetric linear systems
No full textAbstractWe consider projection-minimization methods for solving systems of linear equations. We transform these methods to new ones and show that they converge faster, in some sense. We present, in particular, the transform of the norm decomposition method of Gastinel. The new algorithm presents advantages over some known conjugate-gradient-like methods. This new method is studied, and numerical examples are given
Nonlinear Least-Squares Approach for Large-Scale Algebraic Riccati Equations
No full textInternational audienceWe propose a new optimization approach for solving large-scale continuous-time algebraic Riccati equations with a low-rank right-hand side. First, we project the problem onto a Krylov-type low-dimensional subspace. Then, instead of forcing the orthogonality conditions related to the Galerkin strategy, we minimize the residual to get a low-dimensional nonlinear matrix least-squares problem that will be solved to obtain an approximate factorized solution of the initial Riccati equation. To solve the low-order minimization problems, we propose a globalized Gauss--Newton matrix approach that exhibits a smooth convergence behavior and that guarantees global convergence to stationary points. This novel procedure involves the solution of a linear symmetric matrix problem per iteration that will be solved by direct or preconditioned iterative matrix methods. To illustrate the behavior of the combined scheme, we present numerical results on some test problems
Balanced truncation-rational Krylov methods for model reduction in large scale dynamical systems
No full textInternational audienceIn this paper, we consider the balanced truncation method for model reductions in large-scale linear and time-independent dynamical systems with multi-inputs and multi-outputs. The method is based on the solutions of two large coupled Lyapunov matrix equations when the system is stable or on the computation of stabilizing positive and semi-definite solutions of some continuous-time algebraic Riccati equations when the dynamical system is not stable. Using the rational block Arnoldi, we show how to compute approximate solutions to these large Lyapunov or algebraic Riccati equations. The obtained approximate solutions are given in a factored form and used to build the reduced order model. We give some theoretical results and present numerical examples with some benchmark models
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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