Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exp...Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing and for computing with many espectively. Numerical experiments comparing the proposed method with other existing methods which are MATLAB’s functions expm and funm show that our approach is also very effective and reliable for computing the matrix exponential . Moreover, there are two main advantages of our approach. One is that there is no inverse of a matrix required in this method. The other is that this method is more convenient when computing for a fixed matrix A with many t ≥ 0.展开更多
We are concerned with the numerical methods for nonlinear equation and their semilocal convergence in this paper.The construction techniques of iterative methods are induced by using linear approximation,integral inte...We are concerned with the numerical methods for nonlinear equation and their semilocal convergence in this paper.The construction techniques of iterative methods are induced by using linear approximation,integral interpolation,Adomian series decomposition,Taylor expansion,multi-step iteration,etc.The convergent conditions and proof methods,including majorizing sequences and recurrence relations,in semilocal convergence of iterative methods for nonlinear equations are discussed in the theoretical analysis.The majorizing functions,which are used in majorizing sequences,are also discussed in this paper.展开更多
The modified Hermitian and skew-Hermitian splitting （MHSS） iteration method and preconditioned MHSS （PMHSS） iteration method were introduced respectively. In the paper, on the basis of the MHSS iteration method, w...The modified Hermitian and skew-Hermitian splitting （MHSS） iteration method and preconditioned MHSS （PMHSS） iteration method were introduced respectively. In the paper, on the basis of the MHSS iteration method, we present a PMHSS iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and complex symmetric positive definite/semi-definite matrices. Under suitable conditions, we prove the convergence of the PMHSS iteration method and discuss the spectral properties of the preconditioned matrix. Moreover, to reduce the computing cost, we establish an inexact variant of the PMHSS iteration method and analyze its convergence property in detail. Numerical results show that the PMHSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.展开更多
文摘Matrix Padé approximation is a widely used method for computing matrix functions. In this paper, we apply matrix Padé-type approximation instead of typical Padé approximation to computing the matrix exponential. In our approach the scaling and squaring method is also used to make the approximant more accurate. We present two algorithms for computing and for computing with many espectively. Numerical experiments comparing the proposed method with other existing methods which are MATLAB’s functions expm and funm show that our approach is also very effective and reliable for computing the matrix exponential . Moreover, there are two main advantages of our approach. One is that there is no inverse of a matrix required in this method. The other is that this method is more convenient when computing for a fixed matrix A with many t ≥ 0.
文摘We are concerned with the numerical methods for nonlinear equation and their semilocal convergence in this paper.The construction techniques of iterative methods are induced by using linear approximation,integral interpolation,Adomian series decomposition,Taylor expansion,multi-step iteration,etc.The convergent conditions and proof methods,including majorizing sequences and recurrence relations,in semilocal convergence of iterative methods for nonlinear equations are discussed in the theoretical analysis.The majorizing functions,which are used in majorizing sequences,are also discussed in this paper.
文摘The modified Hermitian and skew-Hermitian splitting （MHSS） iteration method and preconditioned MHSS （PMHSS） iteration method were introduced respectively. In the paper, on the basis of the MHSS iteration method, we present a PMHSS iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and complex symmetric positive definite/semi-definite matrices. Under suitable conditions, we prove the convergence of the PMHSS iteration method and discuss the spectral properties of the preconditioned matrix. Moreover, to reduce the computing cost, we establish an inexact variant of the PMHSS iteration method and analyze its convergence property in detail. Numerical results show that the PMHSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.
