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author | Elizabeth Hunt <elizabeth.hunt@simponic.xyz> | 2023-11-06 10:17:14 -0700 |
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committer | Elizabeth Hunt <elizabeth.hunt@simponic.xyz> | 2023-11-06 10:17:14 -0700 |
commit | 586d8056c1c9e4bb4b8ef219babadc997559b83d (patch) | |
tree | 49845cf9316ec2a72031d770d2a6aa3c5ff4952a | |
parent | fcb00cd96982ba34252046fa35cd0d13ef4387bc (diff) | |
download | cmath-586d8056c1c9e4bb4b8ef219babadc997559b83d.tar.gz cmath-586d8056c1c9e4bb4b8ef219babadc997559b83d.zip |
nov 6, add -lm appended to make test due to my (admittedly heavy) usage of clang
-rw-r--r-- | Makefile | 2 | ||||
-rw-r--r-- | notes/Nov-6.org | 25 |
2 files changed, 26 insertions, 1 deletions
@@ -22,7 +22,7 @@ LDFLAGS := -lm all: $(TEST_EXE) $(TEST_EXE): $(TEST_OBJ) $(LIBRARY) | $(BIN_DIR) - $(CC) $(CPPFLAGS) $(CFLAGS) $(LDFLAGS) $^ -o $@ + $(CC) $(CPPFLAGS) $(CFLAGS) $^ -o $@ $(LDFLAGS) $(LIBRARY): $(OBJ) | $(LIB_DIR) ar rcs $(LIBRARY) $(OBJ_DIR)/*.o 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 |