论文标题
Tridiagonal Toeplitz矩阵的指数：应用和概括
Exponential of tridiagonal Toeplitz matrices: applications and generalization
论文作者
论文摘要
在本文中，提出了一种近似方法，用于计算三角形Toeplitz矩阵的指数。该方法基于某些值在某些值中具有修改的Bessel函数的指数矩阵的近似元素，因此，指数矩阵被分解为对称toeplitz的减法，并且无需使用矩阵乘法的对称hankel矩阵的减法。同样，矩阵由频带矩阵近似，并提供了误差分析以验证该方法。得出了发现块Toeplitz Tridiagonal矩阵和其他一些相关矩阵函数的指数的概括。提出了新想法解决一个和二维热方程的应用，并研究了结果方案的稳定性。数值插图显示了新方法的效率。
In this paper, an approximate method is presented for computing exponential of tridiagonal Toeplitz matrices. The method is based on approximating elements of the exponential matrix with modified Bessel functions of the first kind in certain values and accordingly the exponential matrix is decomposed as subtraction of a symmetric Toeplitz and a persymmetric Hankel matrix with no need for the matrix multiplication. Also, the matrix is approximated by a band matrix and an error analysis is provided to validate the method. Generalizations for finding exponential of block Toeplitz tridiagonal matrices and some other related matrix functions are derived. Applications of the new idea for solving one and two dimensions heat equations are presented and the stability of resulting schemes is investigated. Numerical illustrations show the efficiency of the new methods.
