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24th International conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS) Held as Part of the 21st European Joint conferences on theory and Practice of Software (ETAPS)

作者： Roux, Pierre Iguernlala, Mohamed Conchon, Sylvain Off Natl Etud & Rech Aerosp DTIS F-31055 Toulouse France OCamlPro SAS F-91190 Gif Sur Yvette France Univ Paris Sud LRI F-91405 Orsay France INRIA Saclay Ile de France F-91893 Orsay France

ISBN: (纸本)9783319899633;9783319899633

State-of-the-art (semi-)decision procedures for non-linear real arithmetic address polynomial inequalities by mean of symbolic methods, such as quantifier elimination, or numerical approaches such as interval arithmetic. Although (some of) these methods offer nice completeness properties, their high complexity remains a limit, despite the impressive efficiency of modern implementations. This appears to be an obstacle to the use of SMT solvers when verifying, for instance, functional properties of control-command programs. Using off-the-shelf convex optimization solvers is known to constitute an appealing alternative. However, these solvers only deliver approximate solutions, which means they do not readily provide the soundness expected for applications such as software verification. We thus investigate a-posteriori validation methods and their integration in the SMT framework. Although our early prototype, implemented in the Alt-Ergo SMT solver, often does not prove competitive with state of the art solvers, it already gives some interesting results, particularly on control-command programs.

关键词： SMT Non-linear real arithmetic Polynomial inequalities Convex optimization

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Gauss-Seidel progressive iterative approximation (GS-PIA) for Loop surface interpolation 26

Gauss-Seidel progressive iterative approximation (GS-PIA) fo...

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26th Pacific conference on Computer Graphics and applications, Pacific Graphics 2018

作者： Wang, Zhihao Li, Yajuan Ma, Weiyin Deng, Chongyang School of Sciences Hangzhou Dianzhi University Hangzhou China Department of Mechanical Engineering City University of Hong Kong Hong Kong

ISBN: (纸本)9783038680734

We propose a Gauss-Seidel progressive iterative approximation (GS-PIA) method for Loop subdivision surface interpolation by combining classical Gauss-Seidel iterative method for linear system and progressive iterative approximation (PIA) for data interpolation. We prove that GS-PIA is convergent by applying matrix theory. GS-PIA algorithm retains the good features of the classical PIA method, such as the resemblance with the given mesh and the advantages of both a local method and a global method. Compared with some existed interpolation methods of subdivision surfaces, GS-PIA algorithm has advantages in three aspects. First, it has a faster convergence rate compared with the PIA and WPIA algorithms. Second, compared with WPIA algorithm, GS-PIA algorithm need not to choose weights. Third, GS-PIA need not to modify the mesh topology compared with other methods with fairness measures. numerical examples for Loop subdivision surfaces interpolation illustrated in this paper show the efficiency and effectiveness of GS-PIA algorithm. © 2018 The Author(s).

关键词： linear systems

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Complexity Analysis and Efficient Measurement Selection Primitives for High-Rate Graph SLAM

Complexity Analysis and Efficient Measurement Selection Prim...

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IEEE International conference on Robotics and Automation (ICRA)

作者： Frey, Kristoffer M. Steiner, Ted J. How, Jonathan P. MIT Dept Aeronaut & Astronaut Cambridge MA 02139 USA Draper Tech Staff Cambridge MA 02139 USA

ISBN: (纸本)9781538630815

Sparsity has been widely recognized as crucial for efficient optimization in graph-based SLAM. Because the sparsity and structure of the SLAM graph reflect the set of incorporated measurements, many methods for sparsification have been proposed in hopes of reducing computation. These methods often focus narrowly on reducing edge count without regard for structure at a global level. Such structurally-naive techniques can fail to produce significant computational savings, even after aggressive pruning. In contrast, simple heuristics such as measurement decimation and keyframing are known empirically to produce significant computation reductions. To demonstrate why, we propose a quantitative metric called elimination complexity (EC) that bridges the existing analytic gap between graph structure and computation. EC quantifies the complexity of the primary computational bottleneck: the factorization step of a Gauss-Newton iteration. Using this metric, we show rigorously that decimation and keyframing impose favorable global structures and therefore achieve computation reductions on the order of r(2)/9 and r(3), respectively, where r is the pruning rate. We additionally present numerical results showing EC provides a good approximation of computation in both batch and incremental (iSAM2) optimization and demonstrate that pruning methods promoting globally-efficient structure outperform those that do not.

关键词： Simultaneous localization and mapping Complexity theory Optimization Sparse matrices Extraterrestrial measurements linear algebra"

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Restricted Eigenvalue from Stable Rank with applications to Sparse linear Regression 31

Restricted Eigenvalue from Stable Rank with Applications to ...

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31st Annual conference on Learning theory, COLT 2018

作者： Kasiviswanathan, Shiva Prasad Rudelson, Mark Amazon AWS AI Palo AltoCA United States University of Michigan Ann ArborMI United States

High-dimensional settings, where the data dimension (d) far exceeds the number of observations (n), are common in many statistical and machine learning applications. methods based on 1-relaxation, such as Lasso, are very popular for sparse recovery in these settings. Restricted Eigenvalue (RE) condition is among the weakest, and hence the most general, condition in literature imposed on the Gram matrix that guarantees nice statistical properties for the Lasso estimator. It is hence natural to ask: what families of matrices satisfy the RE condition? Following a line of work in this area (Raskutti et al., 2010;Rudelson and Zhou, 2013;Sivakumar et al., 2015;Oliveira, 2016;Lecué and Mendelson, 2017), we construct a new broad ensemble of dependent random design matrices that have an explicit RE bound. Our construction starts with a fixed (deterministic) matrix X ∈ Rn×d satisfying a simple stable rank condition, and we show that a matrix drawn from the distribution XΦ>Φ, where Φ ∈ Rm×d is a subgaussian random matrix, with high probability, satisfies the RE condition. This construction allows incorporating a fixed matrix that has an easily verifiable condition into the design process, and allows for generation of compressed design matrices that have a lower storage requirement than a standard design matrix. We give two applications of this construction to sparse linear regression problems, including one to a compressed sparse regression setting where the regression algorithm only has access to a compressed representation of a fixed design matrix X. © 2018 S.P. Kasiviswanathan & M. Rudelson.

关键词： Matrix algebra

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numerical Solution of the Boundary Value Problems for Partial Differential Equations. Crash course for holographer

arXiv

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arXiv 2018年

作者： Krikun, Alexander Instituut-Lorentz Universiteit Leiden Delta-ITP P.O. Box 9506 Leiden2300 RA Netherlands

These are the notes for a series of numerical Study group meetings, held in Lorentz institute in the fall of 2017. The aim of the notes is to provide a nonspecialist with the minimal knowledge in numerical methods used in BVP for PDEs, necessary to solve the problems typically arising in applications of holography to condensed matter systems. A graduate level knowledge of linear algebra and theory of Differential Equations is assumed. Special attention is payed to the treatment of the boundary conditions of general form. The notes focus on the practical aspects of the implementation leaving aside the theory behind the methods in use. A few simple problems to test the acquired knowledge are included. Copyright © 2018, The Authors. All rights reserved.

关键词： linear algebra

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20th International Workshop on Computer algebra in Scientific Computing, CASC 2018

20th International Workshop on Computer Algebra in Scientifi...

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20th International Workshop on Computer algebra in Scientific Computing, CASC 2018

ISBN: (纸本)9783319996387

The proceedings contain 25 papers. The special focus in this conference is on Computer algebra in Scientific Computing. The topics include: On a Polytime Factorization Algorithm for Multilinear Polynomials over F2;tropical Newton–Puiseux Polynomials;orthogonal Tropical linear Prevarieties;symbolic-numerical Algorithms forÂ Solving Elliptic Boundary-Value Problems Using Multivariate Simplex Lagrange Elements;symbolic-Numeric Simulation of Satellite Dynamics with Aerodynamic Attitude Control System;finding Multiple Solutions in Nonlinear Integer Programming with algebraic Test-Sets;positive Solutions of Systems of Signed Parametric Polynomial Inequalities;qualitative Analysis of a Dynamical System with Irrational First Integrals;effective Localization Using Double Ideal Quotient and Its Implementation;on Unimodular Matrices of Difference Operators;a Purely Functional Computer algebra System Embedded in Haskell;splitting Permutation Representations ofÂ Finite Groups by Polynomial algebra methods;factoring Multivariate Polynomials with Many Factors and Huge Coefficients;beyond the First Class of Analytic Complexity;a theory and an Algorithm forÂ Computing Sparse Multivariate Polynomial Remainder Sequence;a Blackbox Polynomial System Solver onÂ Parallel Shared Memory Computers;Sparse Polynomial Arithmetic with the BPASÂ Library;computation of Pommaret Bases Using Syzygies;a Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations;symbolic-Numeric methods for Nonlinear Integro-Differential Modeling;a Continuation Method for Visualizing Planar Real algebraic Curves withÂ Singularities;from Exponential Analysis to Padé Approximation and Tensor Decomposition, in One and More Dimensions;Symbolic Algorithm for Generating the Orthonormal Bargmann–Moshinsky Basis for SU(3) Group.

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On generalized positive subdefinite matrices and interior point algorithm 1st

On generalized positive subdefinite matrices and interior po...

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1st International conference on Frontiers in Optimization: theory and applications, FOTA 2016

作者： Das, A.K. Jana, R. Deepmala Indian Statistical Institute 203 B. T. Road Kolkata700108 India Jadavpur University Kolkata700032 India Mathematics Discipline PDPM Indian Institute of Information Technology Design and Manufacturing Jabalpur482005 India

ISBN: (纸本)9789811078132

In this paper, we propose an iterative and descent type interior point method to compute solution of linear complementarity problem LCP(q, A) given that A is real square matrix and q is a real vector. The linear complementarity problem includes many of the optimization problems and applications. In this context, we consider the class of generalized positive subdefinite matrices (GPSBD) which is a generalization of the class of positive subdefinite (PSBD) matrices. Though Lemke’s algorithm is frequently used to solve small and medium-size LCP(q, A), Lemke’s algorithm does not compute solution of all problems. It is known that Lemke’s algorithm is not a polynomial time bound algorithm. We show that the proposed algorithm converges to the solution of LCP(q, A) where A belongs to GPSBD class. We provide the complexity analysis of the proposed algorithm. A numerical example is illustrated to show the performance of the proposed algorithm. © 2018, Springer Nature Singapore Pte Ltd.

关键词： Matrix algebra

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On convergence of numerical methods for optimization problems governed by scalar hyperbolic conservation laws 16th

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16th International conference on Hyperbolic Problems: theory, Numerics and applications, 2016

作者： Herty, Michael Kurganov, Alexander Kurochkin, Dmitry Department of Mathematics RWTH Aachen University Templergraben 55 AachenD-52056 Germany Department of Mathematics Southern University of Science and Technology of China Shenzhen518055 China Mathematics Department Tulane University New OrleansLA70118 United States

ISBN: (纸本)9783319915449

We consider optimization problems governed by scalar hyperbolic conservation laws in one space dimension and study numerical schemes for the solution to arising linear adjoint equations. We analyze convergence properties of adjoint and gradient approximations on an unbounded domain x∈ with a strictly convex flux. This paper provides the theoretical foundation of the scheme introduced in (Herty, Kurganov and Kurochkin, Commun. Math. Sci. 51, 15–48 (2015)) [14]. We also demonstrate that using a higher order temporal discretization helps to substantially improve both the efficiency and accuracy of the overall numerical method. © Springer International Publishing AG, part of Springer Nature 2018.

关键词： Convergence of numerical methods

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A modulus iteration method for retinex problem

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numerical linear algebra WITH applications 2018年第6期25卷

作者： Yang, Xue Huang, Yu-Mei Sun, Li Lanzhou Univ Sch Math & Stat Lanzhou 730000 Gansu Peoples R China

Retinex theory was proposed by Land and McCann, which manifests that the perception of object colors by human eyes is only dependent on the reflectance of the object and unrelated to the illumination amount on the object. Image intensity recorded by digital cameras is the product of reflectance and illumination. The main purpose of the retinex problem is to recover the reflectance from the recorded image just like the human vision system. In this paper, we propose a variational minimization model with physical constraints imposed on reflectance values. We show that the proposed model is equivalent to a linear complementarity problem, and a modulus iteration method is applied to solve it. A large sparse linear system of equations arises in the modulus iteration method. By utilizing the special structure of the coefficient matrix, the solution of the linear system is obtained by solving a smaller linear system of only half of the unknowns. The convergence of the modulus iteration method for solving the linear complementarity problem for the proposed model is also demonstrated. The experiments show that the convergence of the proposed method is much faster than the existing efficient methods for the retinex problem, and the proposed method is also competitive to the existing methods for the retinex problem when considering recovered reflectance quality.

关键词： illumination linear complementarity problem modulus iteration method reflectance retinex problem

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Distributed observer-based cooperative control for output regulation in multi-agent linear parameter-varying systems

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IET CONTROL theory AND applications 2017年第9期11卷 1394-1403页

作者： Mesbahi, Afshin Velni, Javad Mohammadpour Univ Georgia Coll Engn Sch Elect & Comp Engn Athens GA 30602 USA

In this paper, output regulation problem is examined for a class of heterogeneous multi-agent systems, whose dynamics are governed by affine linear parameter-varying (LPV) models, with a known communication topology. In the proposed solution method, the agents are divided into two groups depending on whether or not their output is directly affected by external (such as reference or disturbance) inputs. Conditions for cooperative LPV control synthesis are first constructed through the design of distributed observers. To establish these conditions, the solution to a time-varying Sylvester equation is required. An offline solution to this equation will be proposed to calculate and update the controller state-space matrices. The proposed design methodologies of this study are finally validated using a numerical example.

关键词： observers control system synthesis matrix algebra time-varying systems state-space methods linear parameter varying systems multi-agent systems distributed control distributed observer-based cooperative control multiagent linear parameter-varying systems cooperative LPV control synthesis output regulation problem communication topology distributed observer design time-varying Sylvester equation controller state-space matrices

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