Theory And Solution Of Large And Sparse Matrix Equations In IT Field

In the computational field of science and engineering, many problems finally go to solve the sparse linear equations that has hundreds of thousands of ranks and complete a lot of matrix algebra operations. It's a popular subject in algebra operations nowadays. This paper consists of three parts. First is to analyze and compare several compressed storage methods that are the CSR/CCS method, the JSA method, the Sherman's method, the Ellpack-Itpack method, and their space utilization, and streamline some relevant methods to decrease the storage space and increase the computer speed. The second is to provide the method of congruent diagonalization for large sparse symmetric matrix, it can be realized by computing program. The third is to apply two methods to deal with the sparse linear equations in the convection-diffusion respectively, one is to combine the Cholesky factorization with the iterative method, the other is to combine Pursuit factorization with the iterative method, and provide the corresponding program. With the numerical examples, it shows the methods have good algebra results.