cholesky-growth

At its defaults it draws the growth factor of a 12×12 elimination, against the condition number of the matrix. Three curves against κ. Cholesky's growth factor is exactly 1 at every condition number drawn — the elimination never produces an entry larger than the matrix already had. Partial pivoting on the same matrices reaches the same growth, and reaches it by making up to 9 row interchanges, each of which destroys the symmetry that was the reason to use a symmetric factorisation. The bound the general theory allows, 2^11 = 2048, is drawn above them both.

cholesky-growth is one function in lib/figures/symmetric.js — symmetric eliminations — a growth factor of exactly one, and a diagonal that is zero. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Three curves against κ. Cholesky's growth factor is exactly 1 at every condition number drawn — the elimination never produces an entry larger than the matrix already had. Partial pivoting on the same matrices reaches the same growth, and reaches it by making up to 9 row interchanges, each of which destroys the symmetry that was the reason to use a symmetric factorisation. The bound the general theory allows, 2^11 = 2048, is drawn above them both.

Three curves against κ. Cholesky's growth factor is exactly 1 at every condition number drawn — the elimination never produces an entry larger than the matrix already had. Partial pivoting on the same matrices reaches the same growth, and reaches it by making up to 19 row interchanges, each of which destroys the symmetry that was the reason to use a symmetric factorisation. The bound the general theory allows, 2^23 = 8.4·10⁶, is drawn above them both.

Three curves against κ. Cholesky's growth factor is exactly 1 at every condition number drawn — the elimination never produces an entry larger than the matrix already had. Partial pivoting on the same matrices reaches the same growth, and reaches it by making up to 9 row interchanges, each of which destroys the symmetry that was the reason to use a symmetric factorisation. The bound the general theory allows, 2^11 = 2048, is drawn above them both.

Three curves against κ. Cholesky's growth factor is exactly 1 at every condition number drawn — the elimination never produces an entry larger than the matrix already had. Partial pivoting on the same matrices reaches the same growth, and reaches it by making up to 2 row interchanges, each of which destroys the symmetry that was the reason to use a symmetric factorisation. The bound the general theory allows, 2^4 = 16, is drawn above them both.

Three curves against κ. Cholesky's growth factor is exactly 1 at every condition number drawn — the elimination never produces an entry larger than the matrix already had. Partial pivoting on the same matrices reaches the same growth, and reaches it by making up to 13 row interchanges, each of which destroys the symmetry that was the reason to use a symmetric factorisation. The bound the general theory allows, 2^17 = 1.3·10⁵, is drawn above them both.

Every figure above asserted its own claims on the way to being drawn, and a claim that failed would have failed the build rather than drawn a wrong picture. Those assertions used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

29 distinct claims across 5 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

It draws a decomposition and prints its residual. It calls luFactor, choleskyGrowth, and every figure above carries the badge — which residualcheck verifies by looking for it in the emitted SVG rather than by finding the call that builds one. A badge that is constructed and then left out of the body is the failure that check exists for.

Across the library: the rule bites on 90 of 174 generators — 75 print a residual and 15 are exempt with a published reason; 84 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.