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> tri-diagonal matrices with stencil [-1, 2, -1], Just trying to understand these terms. So is a 5x5 tridiagonal matrix with your stencil look like this?
by xelxebar 3y ago
> tri-diagonal matrices with stencil [-1, 2, -1],
Just trying to understand these terms. So is a 5x5 tridiagonal matrix with your stencil look like this?
2 -1 0 0 0
-1 2 -1 0 0
0 -1 2 -1 0
0 0 -1 2 -1
0 0 0 -1 2
- stabbles 3y agoYeah, exactly. Your matrix shows up when you do a 3-point discretization of -u''(x) = λu(x) with u(0) = u(1) = 0, at 5 equidistant (interior) grid points. That's the discrete, 1D version of the problem they're looking at in the paper. See https://en.wikipedia.org/wiki/Compact_stencil#Three_Point_Stencil_Example https://en.wikipedia.org/wiki/Compact_stencil#Three_Point_St...