# Seidel-Gauss method. international method

Seidel's method (second name - 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.

## The essence of the work

This method is a kind of simplified modification of the Jacobi method. The innovation is that the new value (i)is used immediately upon receipt, not after next iteration. In addition, the convergence and termination conditions 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 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 in working with basic elements. Everything looks pretty simple: a new document is created in the program sheet, the condition is introduced from the very beginningequation and its boundaries, then additional interchangeable elements are explained (if any), after which a compatibility check is prescribed. If it is positive, then the solution algorithm itself is displayed, and only then the output of the roots. Equations can include several stages of solution, each part of which has its own algorithm, mandatory components, interchangeable elements and basic formulas. All this is recorded exclusively in English, without possible analogues. The solution of the equation will be displayed as a ready-made formula or number after saving all the data.

## C++

Seidel's 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 entire problem, but with the termination condition, which is written in three or four stages with the final output of the result. Next, the very 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 for solving the next one. Accounts here are also maintained in English, which cannot be replaced. "C++" is much more complicated than "Pascal", so if you don't have basic knowledge, you shouldn't use it in the first place.

## Summarize

So, the Seidel method is a special way, thanks to which you cansolve 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 eliminates the option of using additional formulas, but at the same time has clear convergence and termination conditions. Strictly established criteria simplify the entire process of work, since if one of the conditions is not met, the program, whether it be Pascal or C++, will simply refuse to further solve the problem.

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