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| author | Elizabeth Hunt <elizabeth.hunt@simponic.xyz> | 2023-12-06 14:15:18 -0700 |
|---|---|---|
| committer | Elizabeth Hunt <elizabeth.hunt@simponic.xyz> | 2023-12-06 14:15:18 -0700 |
| commit | b8c662456f2caf219de2a21f137f8fd61e34b0b2 (patch) | |
| tree | 59e7197a58bedc104f3112e8c6e3a360fa28b0f4 /notes/29-Nov.org | |
| parent | c8bfa7bd0cdb2893f43adc12c74530acc26f4835 (diff) | |
| download | cmath-b8c662456f2caf219de2a21f137f8fd61e34b0b2.tar.gz cmath-b8c662456f2caf219de2a21f137f8fd61e34b0b2.zip | |
fix typos
Diffstat (limited to 'notes/29-Nov.org')
| -rw-r--r-- | notes/29-Nov.org | 20 |
1 files changed, 20 insertions, 0 deletions
diff --git a/notes/29-Nov.org b/notes/29-Nov.org new file mode 100644 index 0000000..a478ebf --- /dev/null +++ b/notes/29-Nov.org @@ -0,0 +1,20 @@ +Jacobi Iteration (cont.) + +x^{k+1} = D^{-1}(b - (L + U)x^k) + +{ + x^{k+1} = x^k + D^-1 r^k + r^{k} = b - Ax^k +} + +error: || x^{k+1} - x^k ||_2 +residual: || r^k ||_2 + +Gauss-Seidel Iteration: +A = (L + D + U) +\Rightarrow Ax = b + (D + U)x = b - Lx + x = (D + U)^-1 (b - Lx) + +x^{k+1} = (D+U)^{-1}(b - Lx^k) +(D + U)^{-1} x (bsubst) |