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

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SUMMARY

The Steepest Descent method is utilized to solve linear systems by minimizing a linear function represented as $f(x_{1},x_{2},...,x_{n}) = \sum_{i=1}^{n} a_{i} x_{i}$. In cases where the function is linear and unconstrained, it is established that a minimum cannot be achieved due to the nature of linear functions. This discussion highlights the limitations of the Steepest Descent method when applied to linear systems without constraints.

PREREQUISITES
  • Understanding of linear algebra concepts
  • Familiarity with optimization techniques
  • Knowledge of the Steepest Descent algorithm
  • Basic proficiency in mathematical notation and functions
NEXT STEPS
  • Study the Steepest Descent algorithm in detail
  • Explore constrained optimization methods
  • Learn about alternative optimization techniques such as Gradient Descent
  • Investigate applications of linear programming
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Mathematicians, data scientists, and engineers interested in optimization methods for linear systems will benefit from this discussion.

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
 
Last edited:
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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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