Cholesky Stability
Why SPD matrices don't need pivoting
Step 1 of 4
Initial State
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Notice the general matrix A has a very small top-left element (0.01), which acts as a bad pivot. The SPD matrix S has its largest elements safely on the diagonal.
General Matrix A (No Pivoting)
Prone to element explosion
0.01
-0.14
0.65
1.52
-0.23
-0.23
1.58
0.77
-0.47
0.54
-0.46
-0.47
0.24
-1.91
-1.72
-0.56
SPD Matrix S (Cholesky)
Bounded Schur complement
3.32
1.35
-0.99
0.28
1.35
2.31
0.29
0.65
-0.99
0.29
3.98
-0.32
0.28
0.65
-0.32
2.40