"线性方程组的迭代法：Jacobi与Gauss-Seidel方法详解"

"The second chapter of the courseware on numerical computation methods focuses on the iterative methods for solving linear systems of equations, including the Jacobi and Gauss-Seidel methods. These methods are used to iteratively compute the solutions to linear systems of equations, following a specific set of steps. The process begins with separating the variables in the equation, which allows for the derivation of an iterative format. The convergence of the iterative format is then assessed to determine if the method will provide accurate results. If the format is deemed to be convergent, the iterative process begins and continues until a set termination condition is met, at which point the iteration stops. The Jacobi method, a specific iterative method, is then discussed in detail. It is used to solve the linear system of equations represented by Ax=b, where A is a non-singular matrix and b is a known vector. The matrix A is transformed into a form consisting of a diagonal matrix, D, and the strictly lower and upper triangular parts of A, denoted as -L and -U, respectively. This transformation facilitates the implementation of the Jacobi method for solving the linear system. Overall, the iterative methods for solving linear systems of equations are an important aspect of numerical computation, allowing for the effective and efficient computation of solutions through iterative processes. The specific steps and methods discussed in the courseware provide a comprehensive understanding of how to approach and solve linear systems of equations using iterative techniques."