The Experts below are selected from a list of 234 Experts worldwide ranked by ideXlab platform

Jianwei Xiao - One of the best experts on this subject based on the ideXlab platform.

  • Randomized Complete Pivoting for Solving Symmetric Indefinite Linear Systems
    SIAM Journal on Matrix Analysis and Applications, 2018
    Co-Authors: Yuehua Feng, Jianwei Xiao
    Abstract:

    The Bunch-Kaufman algorithm and Aasen's algorithm are two of the most widely used methods for solving symmetric indefinite linear systems, yet they both are known to suffer from occasional numerical instability due to potentially exponential element growth or unbounded entries in the matrix factorization. In this work, we develop a randomized Complete Pivoting (RCP) algorithm for solving symmetric indefinite linear systems. RCP is comparable to the Bunch-Kaufman algorithm and Aasen's algorithm in computational efficiency, yet enjoys theoretical element growth and bounded entries in the factorization comparable to that of Complete-Pivoting, up to a theoretical failure probability that exponentially decays with an oversampling parameter. Our finite precision analysis shows that RCP is as numerically stable as Gaussian elimination with Complete Pivoting, and RCP has been observed to be numerically stable in our extensive numerical experiments.

  • randomized Complete Pivoting for solving symmetric indefinite linear systems
    SIAM Journal on Matrix Analysis and Applications, 2018
    Co-Authors: Yuehua Feng, Jianwei Xiao
    Abstract:

    The Bunch--Parlett algorithm, the Bunch--Kaufman algorithm, the bounded Bunch--Kaufman algorithm, and Aasen's algorithm are four well-known methods for solving symmetric indefinite linear systems, ...

Masahiro Fujita - One of the best experts on this subject based on the ideXlab platform.

  • multi terminal binary decision diagrams an efficient datastructure for matrix representation
    Formal Methods, 1997
    Co-Authors: Masahiro Fujita, P C Mcgeer, J Yang
    Abstract:

    In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the BDD representation is often smaller than any other conventional special-case representation: for the n×n Walsh matrix, for example, the BDD representation is of size O(log n). No other special-case representation in common use represents this matrix in space less than O(n²). We describe termwise, row, column, block, and diagonal selection over these matrices, standard an Strassen matrix multiplication, and LU factorization. We demonstrate that the complexity of each of these operations over the BDD representation is no greater than that over any standard representation. Further, we demonstrate that Complete Pivoting is no more difficult over these matrices than partial Pivoting. Finally, we consider an example, the Walsh Spectrum of a Boolean function.

  • Multi-Terminal Binary Decision Diagrams: An Efficient Data Structure for Matrix Representation
    Formal Methods in System Design, 1997
    Co-Authors: Masahiro Fujita, P C Mcgeer, J.c.-y. Yang
    Abstract:

    In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the BDD representation is often smaller than any other conventional special-case representation: for the n×n Walsh matrix, for example, the BDD representation is of size O(log n). No other special-case representation in common use represents this matrix in space less than O(n^2). We describe termwise, row, column, block, and diagonal selection over these matrices, standard an Strassen matrix multiplication, and LU factorization. We demonstrate that the complexity of each of these operations over the BDD representation is no greater than that over any standard representation. Further, we demonstrate that Complete Pivoting is no more difficult over these matrices than partial Pivoting. Finally, we consider an example, the Walsh Spectrum of a Boolean function.

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

  • multi terminal binary decision diagrams an efficient datastructure for matrix representation
    Formal Methods, 1997
    Co-Authors: Masahiro Fujita, P C Mcgeer, J Yang
    Abstract:

    In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the BDD representation is often smaller than any other conventional special-case representation: for the n×n Walsh matrix, for example, the BDD representation is of size O(log n). No other special-case representation in common use represents this matrix in space less than O(n²). We describe termwise, row, column, block, and diagonal selection over these matrices, standard an Strassen matrix multiplication, and LU factorization. We demonstrate that the complexity of each of these operations over the BDD representation is no greater than that over any standard representation. Further, we demonstrate that Complete Pivoting is no more difficult over these matrices than partial Pivoting. Finally, we consider an example, the Walsh Spectrum of a Boolean function.

Yuehua Feng - One of the best experts on this subject based on the ideXlab platform.

  • Randomized Complete Pivoting for Solving Symmetric Indefinite Linear Systems
    SIAM Journal on Matrix Analysis and Applications, 2018
    Co-Authors: Yuehua Feng, Jianwei Xiao
    Abstract:

    The Bunch-Kaufman algorithm and Aasen's algorithm are two of the most widely used methods for solving symmetric indefinite linear systems, yet they both are known to suffer from occasional numerical instability due to potentially exponential element growth or unbounded entries in the matrix factorization. In this work, we develop a randomized Complete Pivoting (RCP) algorithm for solving symmetric indefinite linear systems. RCP is comparable to the Bunch-Kaufman algorithm and Aasen's algorithm in computational efficiency, yet enjoys theoretical element growth and bounded entries in the factorization comparable to that of Complete-Pivoting, up to a theoretical failure probability that exponentially decays with an oversampling parameter. Our finite precision analysis shows that RCP is as numerically stable as Gaussian elimination with Complete Pivoting, and RCP has been observed to be numerically stable in our extensive numerical experiments.

  • randomized Complete Pivoting for solving symmetric indefinite linear systems
    SIAM Journal on Matrix Analysis and Applications, 2018
    Co-Authors: Yuehua Feng, Jianwei Xiao
    Abstract:

    The Bunch--Parlett algorithm, the Bunch--Kaufman algorithm, the bounded Bunch--Kaufman algorithm, and Aasen's algorithm are four well-known methods for solving symmetric indefinite linear systems, ...

J.c.-y. Yang - One of the best experts on this subject based on the ideXlab platform.

  • Multi-Terminal Binary Decision Diagrams: An Efficient Data Structure for Matrix Representation
    Formal Methods in System Design, 1997
    Co-Authors: Masahiro Fujita, P C Mcgeer, J.c.-y. Yang
    Abstract:

    In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the BDD representation is often smaller than any other conventional special-case representation: for the n×n Walsh matrix, for example, the BDD representation is of size O(log n). No other special-case representation in common use represents this matrix in space less than O(n^2). We describe termwise, row, column, block, and diagonal selection over these matrices, standard an Strassen matrix multiplication, and LU factorization. We demonstrate that the complexity of each of these operations over the BDD representation is no greater than that over any standard representation. Further, we demonstrate that Complete Pivoting is no more difficult over these matrices than partial Pivoting. Finally, we consider an example, the Walsh Spectrum of a Boolean function.