summaryrefslogtreecommitdiff
path: root/Homework/math4610/notes/29-Nov.org
diff options
context:
space:
mode:
authorElizabeth Alexander Hunt <me@liz.coffee>2026-07-02 11:55:17 -0700
committerElizabeth Alexander Hunt <me@liz.coffee>2026-07-02 11:55:17 -0700
commit6bf4b90c90f15f4ab60833bddf5b5756d1a6b1f6 (patch)
treeed97e39ec77c5231ffd2c394493e68d00ddac5a4 /Homework/math4610/notes/29-Nov.org
downloadmisc-undergrad-main.tar.gz
misc-undergrad-main.zip
Diffstat (limited to 'Homework/math4610/notes/29-Nov.org')
-rw-r--r--Homework/math4610/notes/29-Nov.org20
1 files changed, 20 insertions, 0 deletions
diff --git a/Homework/math4610/notes/29-Nov.org b/Homework/math4610/notes/29-Nov.org
new file mode 100644
index 0000000..a478ebf
--- /dev/null
+++ b/Homework/math4610/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)