The Experts below are selected from a list of 78 Experts worldwide ranked by ideXlab platform
Juan R Torregrosa - One of the best experts on this subject based on the ideXlab platform.
-
on the convergence of a damped newton like method with modified right hand Side Vector
Applied Mathematics and Computation, 2015Co-Authors: Ioannis K Argyros, Alicia Cordero, Á. Alberto Magreñán, Juan R TorregrosaAbstract:We present a convergence analysis for a damped Newton-like method with modified Right-Hand Side Vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case when the method is defined on R m , our method provides computable error estimates based on the initial data. Such estimates were not given in relevant studies such as. Numerical examples further validating the theoretical results are also presented in this study.
-
on the convergence of a damped secant method with modified right hand Side Vector
Applied Mathematics and Computation, 2015Co-Authors: Ioannis K Argyros, Alicia Cordero, Á. Alberto Magreñán, Juan R TorregrosaAbstract:We present a convergence analysis for a Damped Secant method with modified Right-Hand Side Vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case when the method is defined on R i , our method provides computable error estimates based on the initial data. Such estimates were not given in relevant studies such as (Herceg et al., 1996; Krejic, 2002). Numerical examples further validating the theoretical results are also presented in this study.
Zhenyu Huang - One of the best experts on this subject based on the ideXlab platform.
-
AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids
arXiv: Computational Engineering Finance and Science, 2017Co-Authors: Yu Hong Yeung, Alex Pothen, Mahantesh Halappanavar, Zhenyu HuangAbstract:We present AMPS, an augmented matrix approach to update the solution to a linear system of equations when the matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform N - k contingency analysis, i.e., determine the state of the system when exactly k links from N fail. Our algorithms augment the matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms, a direct method, and a hybrid direct-iterative method for solving the augmented system. We also exploit the sparsity of the matrices and Vectors to accelerate the overall computation. We analyze the time complexity of both algorithms, and show that it is bounded by the number of nonzeros in a subset of the columns of the Cholesky factor that are selected by the nonzeros in the sparse Right-Hand-Side Vector. Our algorithms are compared on three power grids with PARDISO, a parallel direct solver, and CHOLMOD, a direct solver with the ability to modify the Cholesky factors of the matrix. We show that our augmented algorithms outperform PARDISO (by two orders of magnitude), and CHOLMOD (by a factor of up to 5). Further, our algorithms scale better than CHOLMOD as the number of elements updated increases. The solutions are computed with high accuracy. Our algorithms are capable of computing N - k contingency analysis on a 778 thousand bus grid, updating a solution with k = 20 elements in 16 milliseconds on an Intel Xeon processor.
-
AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids
SIAM Journal on Scientific Computing, 2017Co-Authors: Yu Hong Yeung, Alex Pothen, Mahantesh Halappanavar, Zhenyu HuangAbstract:We present AMPS, an augmented matrix approach to update the solution to a linear system of equations when the matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform $N-k$ contingency analysis, i.e., determine the state of the system when exactly $k$ links from $N$ fail. Our algorithms augment the matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms---a direct method and a hybrid direct-iterative method---for solving the augmented system. We also exploit the sparsity of the matrices and Vectors to accelerate the overall computation. We analyze the time complexity of both algorithms and show that it is bounded by the number of nonzeros in a subset of the columns of the Cholesky factor that are selected by the nonzeros in the sparse Right-Hand-Side Vector. Our algorithms are compared on th...
Ioannis K Argyros - One of the best experts on this subject based on the ideXlab platform.
-
on the convergence of a damped newton like method with modified right hand Side Vector
Applied Mathematics and Computation, 2015Co-Authors: Ioannis K Argyros, Alicia Cordero, Á. Alberto Magreñán, Juan R TorregrosaAbstract:We present a convergence analysis for a damped Newton-like method with modified Right-Hand Side Vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case when the method is defined on R m , our method provides computable error estimates based on the initial data. Such estimates were not given in relevant studies such as. Numerical examples further validating the theoretical results are also presented in this study.
-
on the convergence of a damped secant method with modified right hand Side Vector
Applied Mathematics and Computation, 2015Co-Authors: Ioannis K Argyros, Alicia Cordero, Á. Alberto Magreñán, Juan R TorregrosaAbstract:We present a convergence analysis for a Damped Secant method with modified Right-Hand Side Vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case when the method is defined on R i , our method provides computable error estimates based on the initial data. Such estimates were not given in relevant studies such as (Herceg et al., 1996; Krejic, 2002). Numerical examples further validating the theoretical results are also presented in this study.
Yu Hong Yeung - One of the best experts on this subject based on the ideXlab platform.
-
AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids
arXiv: Computational Engineering Finance and Science, 2017Co-Authors: Yu Hong Yeung, Alex Pothen, Mahantesh Halappanavar, Zhenyu HuangAbstract:We present AMPS, an augmented matrix approach to update the solution to a linear system of equations when the matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform N - k contingency analysis, i.e., determine the state of the system when exactly k links from N fail. Our algorithms augment the matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms, a direct method, and a hybrid direct-iterative method for solving the augmented system. We also exploit the sparsity of the matrices and Vectors to accelerate the overall computation. We analyze the time complexity of both algorithms, and show that it is bounded by the number of nonzeros in a subset of the columns of the Cholesky factor that are selected by the nonzeros in the sparse Right-Hand-Side Vector. Our algorithms are compared on three power grids with PARDISO, a parallel direct solver, and CHOLMOD, a direct solver with the ability to modify the Cholesky factors of the matrix. We show that our augmented algorithms outperform PARDISO (by two orders of magnitude), and CHOLMOD (by a factor of up to 5). Further, our algorithms scale better than CHOLMOD as the number of elements updated increases. The solutions are computed with high accuracy. Our algorithms are capable of computing N - k contingency analysis on a 778 thousand bus grid, updating a solution with k = 20 elements in 16 milliseconds on an Intel Xeon processor.
-
AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids
SIAM Journal on Scientific Computing, 2017Co-Authors: Yu Hong Yeung, Alex Pothen, Mahantesh Halappanavar, Zhenyu HuangAbstract:We present AMPS, an augmented matrix approach to update the solution to a linear system of equations when the matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform $N-k$ contingency analysis, i.e., determine the state of the system when exactly $k$ links from $N$ fail. Our algorithms augment the matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms---a direct method and a hybrid direct-iterative method---for solving the augmented system. We also exploit the sparsity of the matrices and Vectors to accelerate the overall computation. We analyze the time complexity of both algorithms and show that it is bounded by the number of nonzeros in a subset of the columns of the Cholesky factor that are selected by the nonzeros in the sparse Right-Hand-Side Vector. Our algorithms are compared on th...
Torregrosa Sánchez, Juan Ramón - One of the best experts on this subject based on the ideXlab platform.
-
On the convergence of a damped Newton-like method with modified right hand Side Vector
'Elsevier BV', 2015Co-Authors: Argyros, Ioannis K., Cordero Barbero Alicia, Magreñán Ruiz, Ángel Alberto, Torregrosa Sánchez, Juan RamónAbstract:[EN] We present a convergence analysis for a damped Newton-like method with modified righthand Side Vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case when the method is defined on Rm, our method provides computable error estimates based on the initial data. Such estimates were not given in relevant studies such as. Numerical examples further validating the theoretical results are also presented in this studyThis research has been supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-{01,02} and partially supported by the Universidad Internacional de La Rioja (UNIR, http://www.unir.net), under the Plan Propio de Investigacion, Desarrollo e Innovacion [2013-2015]. Research group of the third author: Matematica aplicada al mundo real (MAMUR)Argyros, IK.; Cordero Barbero, A.; Magreñán Ruiz, ÁA.; Torregrosa Sánchez, JR. (2015). On the convergence of a damped Newton-like method with modified right hand Side Vector. Applied Mathematics and Computation. 266:927-936. doi:10.1016/j.amc.2015.05.148S92793626
