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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).
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...
I am selling new-like Warne 1" Tactical A404LM Scope Rings (These are high height rings). The rings were purchased new 3 months ago, but have never been used except to mount them on a rifle without ever mounting a scope onto the rings. I am asking $35 cash in Seattle area or $45 shipped with...
Basically bran new condition P365 XMacro Tacops with holster. 30 rounds max down the pipe. This is a beauty and it’s in like new condition. Comes with all the original goodies and a holster. Meet at Tigard Pawn for transfer. Thank you for looking.
This gun is super clean as you can see in the pictures and this video.
Marlin's serial numbers are confusing, but I believe this model with a serial number starting with 03 was manufactured in 1997.
Includer are 4 - 20 counts boxes of ammo.
1 Winchester Ballistic Silver Tip
1 Federal Power...
Sig Sauer P229 chamber in .357sig German made frame
Sig Sauer P229 chambered in .357sig. comes with 2-10rd magazines.
Price is $800. Transfer fees on buyer. Perfer local transfer. No trade.
2002 Honda XR400 in absolutely excellent condition, one of the nicest around. This bike has been cared for meticulously, only trail ridden, never raced, motocrossed etc. It has been nothing short of reliable, as most XRs are, and always had on time maintence. Drivetrain is bone stock. The...
This is a great condition Model 36 Smith that appears to have been manufactured sometime between 1962 and 1966. The bluing is in good shape, with a little wear here and there. I'd rate it 90% minimum. It appears to have been carried at some point, but maybe only a handful of times. Definitely...
I have a pair of new-like Nightforce 34mm X-Treme Duty Ultralite Scope Rings (MEDIUM Height). The rings are just few weeks old and they come in the original retail box. I am asking $130 cash in person, or I could ship with USPS Priority Mail for additional $10. I live in Seattle (Lower Queen Anne).