- #1
Hypatio
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I am trying to figure out how you would write out a matrix for the solution to an equation such as the following:
[tex]\alpha x^{rr}-(2\alpha+2\gamma) x^r+(\alpha+\gamma) x^i+(\beta+\gamma) x^{br}-\beta z^r -(\beta+2\eta) z^b+(\beta+\eta) z^i +\eta z^{bb}=0[/tex]
where alpha, beta, gamma, and eta are coefficients, and x and z are unknowns, and superscripts simply indicate the relative locations of the nodes.
I do not understand how such an equation can possibly have an invertible matrix because for each equation I need to know the x and z values. If I only needed solutions to x or z values, the matrix might look something like this, depending on the values of alpha, beta, etc.:
http://www.eecs.berkeley.edu/~demmel/cs267/lecture17/DiscretePoisson.gif
but I have no idea how to construct a matrix when you need to know two values for each node location.
[tex]\alpha x^{rr}-(2\alpha+2\gamma) x^r+(\alpha+\gamma) x^i+(\beta+\gamma) x^{br}-\beta z^r -(\beta+2\eta) z^b+(\beta+\eta) z^i +\eta z^{bb}=0[/tex]
where alpha, beta, gamma, and eta are coefficients, and x and z are unknowns, and superscripts simply indicate the relative locations of the nodes.
I do not understand how such an equation can possibly have an invertible matrix because for each equation I need to know the x and z values. If I only needed solutions to x or z values, the matrix might look something like this, depending on the values of alpha, beta, etc.:
http://www.eecs.berkeley.edu/~demmel/cs267/lecture17/DiscretePoisson.gif
but I have no idea how to construct a matrix when you need to know two values for each node location.
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