MHB How is the Steepest Descent Formula Used to Solve Linear Systems?

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The discussion focuses on the application of the steepest descent method for solving linear systems. The steepest descent formula is relevant for minimizing functions, particularly when dealing with linear equations. However, it is noted that if the function is purely linear, it lacks a minimum, making the steepest descent approach ineffective in such cases. Participants are seeking clarification on the formula and its application, indicating a need for further resources or links. The conversation highlights the limitations of using steepest descent for linear functions without constraints.
Amer
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Steepest descent for linear system

what is the formula of steep descent to solve linear system
can you give me a link
 
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Re: Steepest descent for linear system

Amer said:
what is the formula of steep descent to solve linear system
can you give me a link

If Your goal is to find the minimum of an $f(x_{1},x_{2},...,x_{n})$ and the $f(*)$ is linear in the $x_{i}$, i.e. it can be written as...

$\displaystyle f(x_{1},x_{2},...,x_{n})= \sum_{i=1}^{n} a_{i}\ x_{i}$ (1)

... where all the $a_{i}$ are constant and You don't have any constrain, then the goal cannot be met because the (1) has no minimum...

Kind regards

$\chi$ $\sigma$
 
Last edited:

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