The weights 8 steps apply, on an operator 8.6% asymmetric
At its defaults it draws the weights 8 steps apply, on an operator 8.6% asymmetric. Two sets of points against the singular-value index, each with the best polynomial of its own parity drawn through it. The bidiagonal method's weights lie on an even polynomial in σ to 1.6·10⁻¹². The Arnoldi method's lie on a general polynomial to 0.063 — which on a symmetric operator is the level of rounding and on this one is 6%.
filter-misfit is one function in lib/figures/lsqrgmres.js —
the other two krylov regularisers — one sequence, two recurrences, and a weight that stops being a function of σ. 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.
At its defaults
Drawn even though every essay passes arguments — which on this site is every essay, at 100% of placements since the standard pass. A default nothing exercises is a trap for the next essay to call this with none, and this is the page where a default that has drifted from the figures around it becomes visible.
Two sets of points against the singular-value index, each with the best polynomial of its own parity drawn through it. The bidiagonal method's weights lie on an even polynomial in σ to 1.6·10⁻¹². The Arnoldi method's lie on a general polynomial to 0.063 — which on a symmetric operator is the level of rounding and on this one is 6%.
m: 8
The arguments are the ones The basis decides what a filter is passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
Two sets of points against the singular-value index, each with the best polynomial of its own parity drawn through it. The bidiagonal method's weights lie on an even polynomial in σ to 1.6·10⁻¹². The Arnoldi method's lie on a general polynomial to 0.063 — which on a symmetric operator is the level of rounding and on this one is 6%.
What it checked while drawing
Every figure above checked its own claims on the way to being drawn, and a claim that failed
would have stopped the picture rather than shipped a wrong one. Those checks 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.
5 distinct claims across 2 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.
a size the reference SVD is affordable at
a step count both methods are still informative at
and the Arnoldi method's are not a function of σ once A is not normal
one of the three operators this family has
the bidiagonal method's weights are an even polynomial in σ
Against the rule
It draws a decomposition and prints its residual. It calls
lstsqQR,
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 217
of 397 generators —
199 print a residual and
18 are exempt with a published reason;
180 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.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.