A Chasing Method for Solving Cyclic Tridiagonal Equations
Ma Min · Keji daobao · 2009
Based on the idea of LU decomposition,the chasing method can be ascribed as the following three steps.Firstly,the coefficient matrix of cyclic tridiagonal equations was decomposed to the multiplication of three matrixes LUD.The matrixes L and U are lower and upper triangular matrix,respectively.While the matrix D is a quasi-diagonal matrix and there are two nonzero entries in the each row of matrix D.Secondly,forward substitution method is used to solve the equation Lu=d,and the backward substitution method is used to solve the equation Uv=u,and then the first and the last row of matrix D are used to solve the unknown variable xn.Now,all the other unknown variables can be solved through backward substitution.The process of matrix decomposition looks like complex,however,the algorithm implement shows that the computational process and programing do not complex.Most important thing is that the total arithmetic operations is O(14n) and smaller than that of the classical algorithms(O(17n)).The statility analysis indicates that the chasing method developed in the paper is stable if the matrix A is diagonally dominant and the condition of 2│ai│≤│bi│are satisfied.The numerical experiments indicate that the numerical results consistent with analytic results.