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

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

$\chi$ $\sigma$
 
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Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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