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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).
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...
Taurus 38 special( not for +P rounds), 6 shot, 2 inch barrel. I do NOT have the box or other goodies, only the Pistol for sale. Excellent condition. Transfer to be done at A CUT ABOVE PAWN in Aloha. Transfer fee is buyers responsibility. No trades. For sale only at this time.
Circa 1950's, Excellent bluing intact, clean wood, take down comes apart clean. Adjustable choke.
Can include a box of ammo.
Consider trades for gold, silver, other guns, shoulder holster for p226 legion, handguns
2021 ram 1500 wheels and tires
6 lug factory dodge wheels with Goodyear wrangler fortitude ht tires
275/65r18 tread is measuring at 5/16 with even wear
Wheels are in amazing condition with zero damage.
Will fit multiple year dodge vehicles.
Here are two really nice and original Israeli IMI Galil magazines for the 223 or 556 caliber rifle. 35 round capacity. All steel. Check out the pics, these are not the junky surplus mags that are commonly seen. The pictured items are the exact mags you'll be getting if you buy these. Cross...
Selling a pair of Salomon Ski Boots. They are for MEN size 29.0.
I bought them brand new and only used them 4 times. The are in LIKE NEW CONDITION. It also comes with the original box too. See pictures
Selling it for $149, price is FIRM and not negotiable. I paid over $450 for these. I accept...
I am selling Vortex Precision 34mm Scope Rings in MINT condition. I purchased these rings at Sportsmen's Warehouse slightly over 3 months ago. The rings come in the original retail box. The rings specs are shown in the second image. I am selling these rings for $80 cash in person (meet in...
Up for sale is my Aero AR-10. It is in beautiful shape, and the 16" barrel only has like 10 rounds down it. It has Radian SD Gasbuster charging handle. Rise Blitz Trigger. No takeup and about a 3.5lb break. A magpul stock, Magpul grip, flip up sights, and comes with 1 hex mag. It has a radian 45...
One last shot at finding this outstanding pistol a new home.
Original owner, sub 1k fired and still in like new condition. Original E2 grips swapped out for factory standard SIG grips. (E2 grips included)
Box, 2 ea. 8 round magazines and all other goodies.
Night sights are strong and bright...
Always kept these with the intention of reading all the articles in
them. There really is very good information in these.
However, my wife says that they have to go and I agree.
I'm old enough that I probably won't manage to read them.
So.... Free! over 250 American Rifleman magazines.
(If...