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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).
Springfield Armory XD Tactical, 5" w/ 1-16rnd factory magazine.
Face to face in Medford, Grants Pass and surrounding areas. No shipping.
Willing to meet half way at agreed upon dealer.
I purchased used and in great condition. Have not fired but gun cycles fine.
Looking to sell quick to fund a...
I'm looking to obtain damaged firearms to be used as training aids. Not operational firearms. Any caliber, size, condition, type of revolver or semi. Feel free to reach out, 210-260-5911.
Up for sale is my Henry AR-7 Survival Rifle in .22 cal. In great condition. Only a couple hundred rounds fired.
The barrel and receiver of this rifle screw off easily to fit inside of the butt stock. As well as two 8 round magazines. Can easily fit in a backpack or duffel bag and assembles in...
Up for sale is my Ruger Charger .22 cal. In excellent condition. Less than 500 rounds fired since purchased new in 2019.
Only things added to the pistol are an after market bolt buffer pin and a flash hider. I will include the stock pin and thread cap as well as a soft case. Also comes with...
Included is holster and soft case if you want them. I got it a few years ago and never used it.
I am open to go down on that price make an offer in private message. I have a pretty good offer from a store but I know they are going to just sell it for what I'm asking
CZ 75B pistol
Mint condition
Two 16-round magazines
Owner's manual and lock
Original case
A classic in CZ 75 family. Bought just two years ago. Several hundreds rounds shot. Field strip after every practice.
$500 OBO. FFL fee on buyer. Meet and transfer at west side of Portland.
SOLD PENDING TRANSFER 11/16/22
Hello,
For sale is an excellent condition Remington 870 Tactical 12 gauge shoots 3" shells and less. I've owned it for almost 15 years. I bought it new and have shot it a few times and kept it clean and lubed and stored in a climate controlled safe.
Nice and all...
I have a used Stack-On 14 Gun Safe. Comes as pictured. In great shape.
Only interested in cash at the moment and I can only meet in Corvallis or Albany. Thank you for looking.
Remington 700 LA 375 Ultra Mag
Talley rings...
50 new pieces of brass,dies are included as well...
This rifle is sitting in a new Bell & Carlson stock,no work performed just set it in it...
The factory synthetic stock is around somewhere...
280 factory new ammunition in Double tap, Barnes...
Original owner with ~1.5k fired.
Pistol is in excellent condition with no dings, nicks, scratches, abnormal wear or blemishes.
-Three 13 round magazines (Oregon sale only)
- Tru Dot night sights added
$450.00 +...
Gun is in excellent condition with about 60 rounds thru it. Includes a Leupold 3.5x10x40 Vari-x 3 scope in perfect condition.
Gun reviewed at - https://www.thetruthaboutguns.com/gun-review-thompsoncenter-icon/
Barrel: 24" 1:10 twist.
Size: 44″ overall length
Weight: 7.75 lbs. empty...
This is an excellent gun! Selling because I’m diving further down the double stack 1911 rabbit hole. Gun is in great condition and I’ve never had one malfunction with it! Holster is also in great condition and perfect for range use or outdoor carry. A great set up! Walk away with everything you...
I have, to the best of my knowledge, a preban, unfired hk91. It's in excellent condition, the real deal. Has telescoping stock, and also the psg1 adjustable stock, swivel bipod, 25 mags, and original and unfired 22 conversion kit, in factory box. The 25 mags also that come with it, are...
Badger Ordnance C1 mount 35mm 1.54" NV height w/J arm and delta point pro mount. Also included new in box delta point pro 12 o'clock mount and ARC riser.
Up for consideration is great looking 1966 Red Seal $100 United States Note. While this is not a “Federal Reserve” note, it remains full legal tender. It also marks the first year of the $100 denomination since the conversion away from large bills in 1928. While I’m no grading expert, I do...
I am selling this upgraded Mark IV Ruger with the carrying case and two 10rd magazines. This Ruger was upgraded for competition with the following mods and it is being sold because it is not being used.
LIST OF UPGRADES
Volquartsen Accurizing Kit, original cost $111.00
Volquartsen Bolt Tuneup...
Please send trade offers and comments thru the contact PM messenger...Thanks
Leupold Mark 8 Rifle Scope 3.5-25 x 56
Leupold Mk 8
Part# 171845
Mil
3.5-25x56 Long Range Scope
ZeroLock
Tremor 3 Reticle
**Lightly Used In Excellent Condition**
$2200 Cash (firm on cash price)
Partial/ Full Trade...