From 586d8056c1c9e4bb4b8ef219babadc997559b83d Mon Sep 17 00:00:00 2001
From: Elizabeth Hunt <elizabeth.hunt@simponic.xyz>
Date: Mon, 6 Nov 2023 10:17:14 -0700
Subject: nov 6, add -lm appended to make test due to my (admittedly heavy)
 usage of clang

---
 notes/Nov-6.org | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)
 create mode 100644 notes/Nov-6.org

(limited to 'notes')

diff --git a/notes/Nov-6.org b/notes/Nov-6.org
new file mode 100644
index 0000000..4a9562f
--- /dev/null
+++ b/notes/Nov-6.org
@@ -0,0 +1,25 @@
+* Power Method
+v_{k+1} = A v_k, k = 0,1,2
+
+** Properties
+1. \frac{A v_k}{||v_k||} \rightarrow v_1
+2. \frac{v_k^T A v_k}{v_k^T v_k} \rightarrow \lambda_1
+3. If \lambda is a n eigenvalue of A, then \frac{1}{\lambda} is an eigenvalue of A^-1
+4. Av = \lambda v
+   Av - \mu v = (\lambda-\mu)v = (A - \mu I)v
+5. If \lambda is an eigenvalue of A, then \lambda - \mu is an eigenvalue of A \cdot \mu I
+
+** Shifting Eigenvalues
+1. Partition [\lambda_n, \lambda_1]
+
+
+* Lanczos Algorithm
+
+#+BEGIN_SRC c
+  for (int i = 0; i < n; i++) {
+    sum = a0;
+    v_dot_v(a[i], x);
+
+    b[i] = sum;
+  }
+#+END_SRC
-- 
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