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condition
In numerical analysis, the condition number of a function measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive a function is to changes or errors in the input, and how much error in the output results from an error in the input. Very frequently, one is solving the inverse problem: given
f
(
x
)
=
y
,
{\displaystyle f(x)=y,}
one is solving for x, and thus the condition number of the (local) inverse must be used. In linear regression the condition number of the moment matrix can be used as a diagnostic for multicollinearity.The condition number is an application of the derivative, and is formally defined as the value of the asymptotic worst-case relative change in output for a relative change in input. The "function" is the solution of a problem and the "arguments" are the data in the problem. The condition number is frequently applied to questions in linear algebra, in which case the derivative is straightforward but the error could be in many different directions, and is thus computed from the geometry of the matrix. More generally, condition numbers can be defined for non-linear functions in several variables.
A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. In non-mathematical terms, an ill-conditioned problem is one where, for a small change in the inputs (the independent variables) there is a large change in the answer or dependent variable. This means that the correct solution/answer to the equation becomes hard to find. The condition number is a property of the problem. Paired with the problem are any number of algorithms that can be used to solve the problem, that is, to calculate the solution. Some algorithms have a property called backward stability. In general, a backward stable algorithm can be expected to accurately solve well-conditioned problems. Numerical analysis textbooks give formulas for the condition numbers of problems and identify known backward stable algorithms.
As a rule of thumb, if the condition number
κ
(
A
)
=
10
k
{\displaystyle \kappa (A)=10^{k}}
, then you may lose up to
k
{\displaystyle k}
digits of accuracy on top of what would be lost to the numerical method due to loss of precision from arithmetic methods. However, the condition number does not give the exact value of the maximum inaccuracy that may occur in the algorithm. It generally just bounds it with an estimate (whose computed value depends on the choice of the norm to measure the inaccuracy).
Selling a wingmaster barrel in excellent condition. Was the original on my 870 (late 1960s serial) and is in awesome condition. Bluing looks new. 2 3/4 only and had a polychoke on it. $200
I’m looking to buy a Kriss vector in
( 9mm carbine ) not the pistol with the folding stock not the AR collapsible stock also id rather buy it used as to keep my cost down but if it’s under the retail price that would be great.any extras are a plus.
I may be open to a vector 9 mm pistol for the...
I'm selling my bullet safe bulletproof vest size large it's an excellent condition only worn a few times. Level 3A price is 300 cash firm no sales tax no delivery fee.
For sale is a Sig P365 (9mm) with 3 magazines (on flush, 2 extended) and tritium night sights. Comes with original box, all paperwork, all stickers. It has been test fired only and was never carried. It has no holster wear and is in immaculate like new condition. Price is $400. Location is...
For sale is a Beretta M9A3 (9mm Luger) in flat dark earth. Comes in original box with all original paperwork, stickers, manual, cable lock, tritium night sights and three 17 rd mags. It is suppressor ready out of box. In my opinion it is the best suppressor host on the market, about 5-10 db's...
Holosun HM3X great condition hardly used, has one small scuff on the top on the top, comes with the original box.
Asking $140
Can meet in Oregon City / Happy Valley
503-887-7600
I've got an XD 45 Tactical from Springfield Armory for sale. Less than 300 rounds through it, it's in very good condition. It has some wear marks on the slide from being holstered and upholstered. You also get the original case which contains a spare mag holder, mag loader, a formed plastic...
Selling my G43 due to lack of use. I have larger carry guns that I prefer. It's in like new condition, probably fewer than 100 rounds total through it.
All stock, no modifications. Comes with two extra magazines. Does not come with original box.
Not interested in any trades, cash only. Can...
Trade Glock 17, less than 200 rds, 4 mags, IWB holster, great condition.
Looking for more concealable handgun or $500. Examples Glock 19, Glock 43x, FN 9, or any interesting offer. Please reply with any questions.
I bought this DD MK12 in 2014 as a grail gun. But my interest and needs have changed. It has about 500 rounds through it, probably closer to 400. Mostly a range gun, never abused. Diligently cleaned and cared for, it's like new. Has a battlecomp on front and I'll put the original stock on for...
Going to keep it short since this one hurts.
CZ 97
2 mags
Wrench
Original box
I’m original purchaser and have put less than 100rds thru currently. I’ll likely take it for another spin (20-50rds) before sending it off. It is ridiculously accurate.
$850 cash at Portland FFL with all fees on...
S&W Model 41 Performance Center. This has been a range toy. About 1k rounds through it, great condition.
Comes with original box with factory stuff and three (3) mags.
Transfer at A Cut Above or Adaptive Firing Solutions, unless we can agree on another place. Unqualified "I'll take it" in...
I've got an XD 45 Tactical from Springfield Armory for sale. Less than 300 rounds through it, it's in very good condition. It has some wear marks on the slide from being holstered and upholstered. You also get the original case which contains a spare mag holder, mag loader, a formed plastic...
I have this old Remington 1902 Rolling Block rifle for sale. All original EXCEPT the old steel buttplate was removed and replaced with a rubber butt pad. Its a 7mm Mauser I think which is 7x57mm. Seeing as it was made after 1898 we have to go an FFL dealer to transfer it. My preferred FFL dealer...