The Seidel method (the second name is Gauss-Seidel) is a classic international method with which you can solve various systems of linear equations. Now we will talk about this in more detail.
Essence of the work
This method is a kind of simplified modification of the Jacobi method. The innovation is that the new meaning ( i) used immediately after receipt, and not after the next iteration. In addition, the conditions for convergence and termination are clearly defined, the violation of which will lead to an incorrect answer to the equation. The Seidel method, an example of which we have provided in the picture, not only simplifies the solution process, but also speeds it up. Therefore, it is actively used by programmers to create and solve complex systems.
Seidel's method. "Pascal"
No programmer can do without mathematical formulas and equations. And this means that the Seidel method is actively used in the Pascal program to gain experience with robots with basic elements. Everything looks pretty simple: a new document is created in the program sheet, the condition of the equation and its boundaries are introduced from the very beginning, then additional replaceable elements (if any) are explained, then a compatibility check is written. If it is positive, then the solution algorithm itself is output, and only then the root derivation . Equations can include several stages of a solution, each part of which has its own algorithm, mandatory constituent, replaceable elements and basic formulas. All this is written exclusively in English, without possible analogues. The solution to the equation will be displayed in the form of a ready-made formula or number after saving all the data.
"C ++"
The Seidel method is also widely used in the "C ++" program, but here everything is completely different than in "Pascal". The equation in "C ++" does not begin with the condition of the whole problem, but with the termination condition, which is prescribed in three or four stages with the final conclusion of the result. Next, the course of the solution is prescribed using this method, describing in detail all the unknowns, after which a formula is derived in order to prove the equality between the two results of the equation. The condition is that each value of the previous one is necessary to solve the next. Accounts are also maintained in English, which cannot be replaced. "C ++" is much more complicated than "Pascal", therefore, without basic knowledge, it should not be used initially.
To summarize
So, the Seidel method is a special way, thanks to which it is possible to solve systems of linear equations of any complexity. Most often, it is the base for programs such as Pascal and C ++. This is a kind of improved modification of the Jacobi method, which excludes the option of using additional formulas, but at the same time has clear conditions for convergence and end. Strictly established criteria simplify the whole process of work, because if one of the conditions is not fulfilled, the program, whether it be Pascal or C ++, will simply refuse to further solve the problem.