在高斯消去法中,我们试图将原n元线性方程组消减为三角形(又称上...（In the Gauss elimination method, we try to reduce the original n system of linear equations to a triangle...）.doc

在高斯消去法中,我们试图将原n元线性方程组消减为三角形(又称上...（In the Gauss elimination method, we try to reduce the original n system of linear equations to a triangle...） In the Gauss elimination method, we try to reduce the original n linear system of equations to a triangle (also called a triangle). In triangular matrices, the coefficients of the matrix elements under the diagonal are 0. For the Gauss elimination method, the most useful is the triangular matrix whose lines are 1 diagonal elements after standardized processing. Fig. 8.15 is the original equation in the form of normalized triangular matrix. The coefficients of the coefficients on the diagonal (color) and the components of the vector Y are no longer the original values. The 3 equations corresponding to Fig. 8.15 are: X1+x2+x3=4 X2-x3=1 X3=4 This set of equations was solved is quite simple: the last solution equation X3 (X3 = 1), which will be substituted into the above equation by x2 (x2 = 2), and then put these two values into the first equation by X1 (x1 = 1). This process is called back generation. The Gauss elimination algorithm follows. 1 Gauss elimination algorithm Transform the original equations into standard matrices; Solving xi. by back substitution method EMBED Equation.3 * EMBED Equation.3 EMBED Equation.3. Fig. 8.15 primitive equation in standard triangular matrix 2 augmented matrix Before continuing to study the content, we have to determine which data structure is used to represent the n linear system of equations with n unknowns. A widely adopted method for representing such equations is the augmented matrix. This special representation can make the triangulation of matrix and the programming of backtracking more concise. In Figure 8.16, the augmented matrix form of the n system of linear equations with n unknowns is given. The augmented matrix can be represented by a two-dimensional array of Aug. Note that the augmented matrix n n+1 column, the last column of the augmented matrix (with color mark) is a consta