Environmental Data Analysis by Zhang Zhihua

Author:Zhang, Zhihua
Language: eng
Format: epub
Publisher: De Gruyter
Published: 2017-03-13T04:00:00+00:00

If the Jacobian determinant

then the solution is

Continue this procedure, in general, starting from (xk , yk), if

the solution is

This gives the iterative process.

If max{ |xN+1 − xN |, |yN+1 − yN |} < ε. Then (xN+1, yN+1) is a desired solution.

6.3.4Iterative method to solve systems of linear equations

Consider a system of linear equations

Thematrix form is Ax = b ,where A = (aij)n×n , x = (x1, . . . , xn)T, and b = (b1, . . . , bn)T .

(a)Jacobian iterative method

The system of linear equations (6.3.2) can be rewritten in the form

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