In this paper, we establish a class of sparse update algorithm based on matrix triangular factorizations for solving a system of sparse equations. The local Q-superlinear convergence of the algorithm is proved without...In this paper, we establish a class of sparse update algorithm based on matrix triangular factorizations for solving a system of sparse equations. The local Q-superlinear convergence of the algorithm is proved without introducing an m-step refactorization. We compare the numerical results of the new algorithm with those of the known algorithms, The comparison implies that the new algorithm is satisfactory.展开更多
In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of non...In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of nonzero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner. To overcome this difficulty, we define a new storage scheme for general sparse matrices in this paper. With the new storage scheme, we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.In Section 1, we provide an introduction to the addressed problem and the interval Newton's methods. In Section 2, some currently used storage schemes for sparse sys-terns are reviewed. In Section 3, new index schemes to store general sparse matrices are reported. In Section 4, we present a parallel algorithm to evaluate a general sparse Jarobian matrix. In Section 5, we present a parallel algorithm to solve the correspond-ing interval linear 8ystem by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.展开更多
文摘In this paper, we establish a class of sparse update algorithm based on matrix triangular factorizations for solving a system of sparse equations. The local Q-superlinear convergence of the algorithm is proved without introducing an m-step refactorization. We compare the numerical results of the new algorithm with those of the known algorithms, The comparison implies that the new algorithm is satisfactory.
文摘In solving application problems, many largesscale nonlinear systems of equations result in sparse Jacobian matrices. Such nonlinear systems are called sparse nonlinear systems. The irregularity of the locations of nonzero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner. To overcome this difficulty, we define a new storage scheme for general sparse matrices in this paper. With the new storage scheme, we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.In Section 1, we provide an introduction to the addressed problem and the interval Newton's methods. In Section 2, some currently used storage schemes for sparse sys-terns are reviewed. In Section 3, new index schemes to store general sparse matrices are reported. In Section 4, we present a parallel algorithm to evaluate a general sparse Jarobian matrix. In Section 5, we present a parallel algorithm to solve the correspond-ing interval linear 8ystem by the all-row preconditioned scheme. Conclusions and future work are discussed in Section 6.
