The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform

Hans D. Mittelmann - One of the best experts on this subject based on the ideXlab platform.

  • Polynomial-Time Methods to Solve Unimodular Quadratic Programs With Performance Guarantees
    IEEE Transactions on Aerospace and Electronic Systems, 2019
    Co-Authors: Shankarachary Ragi, Edwin K. P. Chong, Hans D. Mittelmann
    Abstract:

    We develop polynomial-time heuristic methods to solve unimodular quadratic program (UQP) approximately, which is a known non-deterministic polynomial-time hard (NP-hard) problem. Several problems in active sensing and wireless communication applications boil down to UQPs. First, we derive a performance bound for a known UQP approximation method called Dominant Eigenvector matching heuristic. Next, we present two new polynomial-time heuristic methods inspired from the greedy strategy, and we provide performance guarantees for these methods with respect to the optimal objective.

  • Polynomial-Time Methods to Solve Unimodular Quadratic Programs With Performance Guarantees
    arXiv: Optimization and Control, 2017
    Co-Authors: Shankarachary Ragi, Edwin K. P. Chong, Hans D. Mittelmann
    Abstract:

    We develop polynomial-time heuristic methods to solve unimodular quadratic programs (UQPs) approximately, which are known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present three new heuristic methods with polynomial-time complexity to solve the UQP approximately. The first method is called Dominant-Eigenvector-matching; here the solution is picked that matches the complex arguments of the Dominant Eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second method, a greedy strategy, is shown to provide a performance guarantee of (1-1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. The third heuristic method is called row-swap greedy strategy, which is an extension to the greedy strategy and utilizes certain properties of the UQP to provide a better performance than the greedy strategy at the expense of an increase in computational complexity. We present numerical results to demonstrate the performance of these heuristic methods, and also compare the performance of these methods against a standard heuristic method called semidefinite relaxation.

  • Heuristic methods for designing unimodular code sequences with performance guarantees
    2017 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2017
    Co-Authors: Shankarachary Ragi, Edwin K. P. Chong, Hans D. Mittelmann
    Abstract:

    We develop polynomial-time heuristic methods to solve unimodular quadratic programming (UQP) approximately, which is known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present two new heuristic methods with polynomial complexity to solve the UQP approximately. The first method is called Dominant-Eigenvector-matching; here the solution is picked that matches the complex arguments of the Dominant Eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second heuristic method, a greedy strategy, is shown to provide a performance guarantee of (1 - 1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. We also present results from simulations to demonstrate the performance of these heuristic methods.

  • ICASSP - Heuristic methods for designing unimodular code sequences with performance guarantees
    2017 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2017
    Co-Authors: Shankarachary Ragi, Edwin K. P. Chong, Hans D. Mittelmann
    Abstract:

    We develop polynomial-time heuristic methods to solve unimodular quadratic programming (UQP) approximately, which is known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present two new heuristic methods with polynomial complexity to solve the UQP approximately. The first method is called Dominant-Eigenvector-matching; here the solution is picked that matches the complex arguments of the Dominant Eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second heuristic method, a greedy strategy, is shown to provide a performance guarantee of (1 − 1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. We also present results from simulations to demonstrate the performance of these heuristic methods.

Michael J Panza - One of the best experts on this subject based on the ideXlab platform.

  • application of power method and Dominant Eigenvector eigenvalue concept for approximate eigenspace solutions to mechanical engineering algebraic systems
    American journal of mechanical engineering, 2018
    Co-Authors: Michael J Panza
    Abstract:

    This paper shows how the concept of Dominant Eigenvector/eigenvalue and the power method can be used for understanding the solution to practical problems in a broad class of mechanical engineering systems described by linear algebraic equations. An analytical mathematical procedure is developed to obtain a reasonably accurate approximate eigenspace solution to the system Ax=b by transforming the non-symmetric system matrix into a form where the power method is used several times to compute the contribution of only one or two Eigenvector/eigenvalue pairs that dominate the solution. The complete set of eigenvalues and Eigenvectors is not required. The intent is to provide a novel application of and show the importance of the significance of Dominant Eigenvector/eigenvalue pairs and to use the power method in the analysis and understanding of mechanical engineering systems for both education and practice. Typically, the concepts of both Eigenvector expansion and Dominant contribution are not included in mechanical engineering education. The scope of application is a broad area of six practical mechanical engineering problems including translational and rotational dynamics, statics of structures, thermal energy balance, fluid continuity, and feedback control. These general mechanical engineering systems naturally contain numerical A and b matrices that fit the scope suitable for providing feasible accuracy. The systems range from fourth order to two hundredth order. Results indicate that accuracy greatly improves as the A matrix contains elements of the same order of numerical magnitude, either naturally from the physics of the problem, or through a transformation to dimensionless parameters. Motivation for using the power method for Dominant Eigenvector/eigenvalue calculation comes from methods used in web page rank algorithms and a desire to expand mechanical engineering students’ education in understanding the role of the eigenstate expansion method for the solution of algebraic equations without computing all of its eigenvalues and Eigenvectors. An in depth quantitative assessment of the approximate Dominant eigenspace method accuracy is obtained by testing the mechanical engineering examples against a near exact solution via a software solver. This error assessment is based on parameters useful in the design and understanding of mechanical systems. The accuracy achieved is feasible for education and for other uses of the method by practicing mechanical engineers such as when a simple analytical based approximate model may be more suited for inclusion into larger system based models.

  • Application of Power Method and Dominant Eigenvector/Eigenvalue Concept for Approximate Eigenspace Solutions to Mechanical Engineering Algebraic Systems
    American journal of mechanical engineering, 2018
    Co-Authors: Michael J Panza
    Abstract:

    This paper shows how the concept of Dominant Eigenvector/eigenvalue and the power method can be used for understanding the solution to practical problems in a broad class of mechanical engineering systems described by linear algebraic equations. An analytical mathematical procedure is developed to obtain a reasonably accurate approximate eigenspace solution to the system Ax=b by transforming the non-symmetric system matrix into a form where the power method is used several times to compute the contribution of only one or two Eigenvector/eigenvalue pairs that dominate the solution. The complete set of eigenvalues and Eigenvectors is not required. The intent is to provide a novel application of and show the importance of the significance of Dominant Eigenvector/eigenvalue pairs and to use the power method in the analysis and understanding of mechanical engineering systems for both education and practice. Typically, the concepts of both Eigenvector expansion and Dominant contribution are not included in mechanical engineering education. The scope of application is a broad area of six practical mechanical engineering problems including translational and rotational dynamics, statics of structures, thermal energy balance, fluid continuity, and feedback control. These general mechanical engineering systems naturally contain numerical A and b matrices that fit the scope suitable for providing feasible accuracy. The systems range from fourth order to two hundredth order. Results indicate that accuracy greatly improves as the A matrix contains elements of the same order of numerical magnitude, either naturally from the physics of the problem, or through a transformation to dimensionless parameters. Motivation for using the power method for Dominant Eigenvector/eigenvalue calculation comes from methods used in web page rank algorithms and a desire to expand mechanical engineering students’ education in understanding the role of the eigenstate expansion method for the solution of algebraic equations without computing all of its eigenvalues and Eigenvectors. An in depth quantitative assessment of the approximate Dominant eigenspace method accuracy is obtained by testing the mechanical engineering examples against a near exact solution via a software solver. This error assessment is based on parameters useful in the design and understanding of mechanical systems. The accuracy achieved is feasible for education and for other uses of the method by practicing mechanical engineers such as when a simple analytical based approximate model may be more suited for inclusion into larger system based models.

A.n. Willson - One of the best experts on this subject based on the ideXlab platform.

Fan Xu - One of the best experts on this subject based on the ideXlab platform.

  • Analysis and VLSI Realization of a Blind Beamforming Algorithm
    Journal of VLSI signal processing systems for signal image and video technology, 2005
    Co-Authors: Fan Xu, Guichang Zhong, Alan N. Willson
    Abstract:

    We present the fixed-point analysis and VLSI realization of a maximum-power blind beamforming algorithm. This algorithm consists of the computation of a correlation matrix and its Dominant Eigenvector, and we propose that the latter be accomplished by the power method. After analyzing the numerical stability of the power method, we derive a division-free form of the algorithm. Based on a block-Toeplitz assumption, we design an FIR filter based system to realize both the correlation computation and the power method. Our ring processor, which is optimized to implement digital filters, is used as the core of the architecture. A special technique for dynamically switching filter inputs is shown to double the system throughput. VLSI design is discussed in detail and chip fabrication results are presented.

  • Efficient hardware architectures for Eigenvector and signal subspace estimation
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2004
    Co-Authors: Fan Xu, A.n. Willson
    Abstract:

    We consider hardware solutions to the adaptive-signal subspace-estimation problem. In deriving a hardware-realizable subspace tracking algorithm, we have applied delayed updating to the PASTd algorithm to achieve high speed. Pipelined and systolic architectures and the estimation of the Dominant Eigenvector or the signal subspace are also studied. Methods for approximating a reciprocal computation are employed and simulation results are presented to validate our algorithm and hardware architectures.

  • Local stability analysis and hardware realization of an Eigenvector tracking algorithm
    ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 2001
    Co-Authors: Fan Xu, A.n. Willson
    Abstract:

    We present a mathematical analysis of the DPAST algorithm for estimating the Dominant Eigenvector of a data correlation matrix. It is shown that delayed updating does not affect the algorithm's local stability. A high-speed and division-free implementation of the algorithm is also discussed. Furthermore, we give simulation results for the algorithm.

  • ISCAS (2) - Local stability analysis and hardware realization of an Eigenvector tracking algorithm
    ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 2001
    Co-Authors: Fan Xu, A.n. Willson
    Abstract:

    We present a mathematical analysis of the DPAST algorithm for estimating the Dominant Eigenvector of a data correlation matrix. It is shown that delayed updating does not affect the algorithm's local stability. A high-speed and division-free implementation of the algorithm is also discussed. Furthermore, we give simulation results for the algorithm.

  • Fixed-point analysis and realization of a blind beamforming algorithm
    Advanced Signal Processing Algorithms Architectures and Implementations IX, 1999
    Co-Authors: Fan Xu, Dengwei Fu, Alan N. Willson
    Abstract:

    We present the fixed-point analysis and realization of a blind beamforming algorithm. This maximum-power beamforming algorithm consists of the computation of a correlation matrix and its Dominant Eigenvector, and we propose that the later be accomplished by the power method. After analyzing the numerical stability of the power method, we derive a division-free form of the algorithm. Based on a block-Toeplitz assumption, we design an FIR filter based system to realize both the correlation computation and the power method. Our ring processor, which is optimized to implement digital filters, is used as the core of the architecture. A special technique for dynamically switching filter inputs is shown to double the system throughput. Finally we discuss the issue of hardware/software hybrid realization.

Shankarachary Ragi - One of the best experts on this subject based on the ideXlab platform.

  • Polynomial-Time Methods to Solve Unimodular Quadratic Programs With Performance Guarantees
    IEEE Transactions on Aerospace and Electronic Systems, 2019
    Co-Authors: Shankarachary Ragi, Edwin K. P. Chong, Hans D. Mittelmann
    Abstract:

    We develop polynomial-time heuristic methods to solve unimodular quadratic program (UQP) approximately, which is a known non-deterministic polynomial-time hard (NP-hard) problem. Several problems in active sensing and wireless communication applications boil down to UQPs. First, we derive a performance bound for a known UQP approximation method called Dominant Eigenvector matching heuristic. Next, we present two new polynomial-time heuristic methods inspired from the greedy strategy, and we provide performance guarantees for these methods with respect to the optimal objective.

  • Polynomial-Time Methods to Solve Unimodular Quadratic Programs With Performance Guarantees
    arXiv: Optimization and Control, 2017
    Co-Authors: Shankarachary Ragi, Edwin K. P. Chong, Hans D. Mittelmann
    Abstract:

    We develop polynomial-time heuristic methods to solve unimodular quadratic programs (UQPs) approximately, which are known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present three new heuristic methods with polynomial-time complexity to solve the UQP approximately. The first method is called Dominant-Eigenvector-matching; here the solution is picked that matches the complex arguments of the Dominant Eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second method, a greedy strategy, is shown to provide a performance guarantee of (1-1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. The third heuristic method is called row-swap greedy strategy, which is an extension to the greedy strategy and utilizes certain properties of the UQP to provide a better performance than the greedy strategy at the expense of an increase in computational complexity. We present numerical results to demonstrate the performance of these heuristic methods, and also compare the performance of these methods against a standard heuristic method called semidefinite relaxation.

  • Heuristic methods for designing unimodular code sequences with performance guarantees
    2017 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2017
    Co-Authors: Shankarachary Ragi, Edwin K. P. Chong, Hans D. Mittelmann
    Abstract:

    We develop polynomial-time heuristic methods to solve unimodular quadratic programming (UQP) approximately, which is known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present two new heuristic methods with polynomial complexity to solve the UQP approximately. The first method is called Dominant-Eigenvector-matching; here the solution is picked that matches the complex arguments of the Dominant Eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second heuristic method, a greedy strategy, is shown to provide a performance guarantee of (1 - 1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. We also present results from simulations to demonstrate the performance of these heuristic methods.

  • ICASSP - Heuristic methods for designing unimodular code sequences with performance guarantees
    2017 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2017
    Co-Authors: Shankarachary Ragi, Edwin K. P. Chong, Hans D. Mittelmann
    Abstract:

    We develop polynomial-time heuristic methods to solve unimodular quadratic programming (UQP) approximately, which is known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present two new heuristic methods with polynomial complexity to solve the UQP approximately. The first method is called Dominant-Eigenvector-matching; here the solution is picked that matches the complex arguments of the Dominant Eigenvector of the Hermitian matrix in the UQP formulation. We also provide a performance guarantee for this method. The second heuristic method, a greedy strategy, is shown to provide a performance guarantee of (1 − 1/e) with respect to the optimal objective value given that the objective function possesses a property called string submodularity. We also present results from simulations to demonstrate the performance of these heuristic methods.