The Computation Of Pentadiagonal Toeplitz Matrix

Toeplitz matrix is a kind of special matrix, which is widely applied in digital signal pro-cessing and other fields. In recent years, the calculation of Toeplitz matrix has been extensively studied. Based on the structural characteristics of penta-diagonal Toeplitz matrix and the pe-riodic penta-diagonal Toeplitz matrix, this paper investigates the calculation methods of deter-minant, inverse matrix and solution of linear equations. Accordingly, some new algorithms are presented.For the penta-diagonal Toeplitz matrix, some new computational algorithms are investigat-ed by its structural characteristics, such as the permutation of matrix rows and columns, the thought of dividing matrix to blocks and the method of bordered matrix etc.. Then some new methods are proposed for the calculations of determinant, inverse matrix and the algorithm of linear equations. Meanwhile, the feasibility of the methods and the effectiveness of the algo-rithms are verified through some numerical examples.Thanks to the special characteristics of periodic penta-diagonal Toeplitz matrix. By using the matrix blocks method and matrix reduction technique, some new computational algorithms of the matrix determinant, inverse matrix and linear equations algorithm are presented. Fur-thermore, some numerical examples are given to illustrate that the algorithms are effective and feasible.