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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).
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...
Please Note: $140 for Bare Bow or $220 for Setup as shown in the Photo's
Sold Pending Funds
70lb L.H. Bear Encounter Compound Bow
All set up and ready to shoot
It is set at 29" draw but the module can be re-positioned for longer or shorter draw
Comes as you see in the photo and includes a...
Hello everyone,
I have a Vortex Viper PST gen 2 5-25x50mm scope in mil/mil with EBR7C reticle.
Scope is $1070 brand new on optics planet right now and was mounted on and zeroed but never taken into the field.
It's in great condition.
Comes with Nightforce Ultralight 1.125" ring ($170) and Vortex...
Nice clean Harris Bipod that came with a used rifle that I bought. Needs a new home. Bipod in pics is the exact one that you will receive. Cross posted so First I'll take it followed by an IM or email gets the goods. Several payment options available. Thanks for looking!
$500
27" barrel
Very nice condition, I bought it from a friend a couple years ago, who bought it new, he said he only used it a couple times, always cleaned and put away properly.
45 cal, brass trimmings, patch box has a jag inside.
Any trade needs at least $200 cash in wth the trades...
Kimber Micro 380 - Excellent Condition - $475
Less than 500 rounds. 3, 7 round magazines. DeSantis Gun Hide holster. Case and box. Shoots great, just need funds for next purchase.
**SPF to Buster Beaver** I have an absolutely beautiful HK91 with IB (1981) date code available for sale. This rifle has seen very little use and is in excellent almost as-new condition overall. There are some signs of use but very little although it does look like it may have had a claw mount...
Ruger 57 5.7x28mm 4.94in Black Nitride Pistol - 20+1 Rounds GREAT CONDITION ONLY 100 ROUNDS FIRED
Pistol is three years old. Mostly shot in doors using a custom 57 laser bullet.
Comes with loader, two 20 round magazines, security lock, manufacturers booklet.
Will meet to at any gun shop...
Nash 24B, 28’8 overall length. This is an ‘Off the Grid’ model meaning oversized holding and propane tanks. Solar powered batteries run everything except air and microwave. Plug in or generator(not included) to power them. Has mud grip tires, power jack, super bright front and back ‘work...
This one is $1,500 cash. No trades. I'll throw in a box of shells too. No, it has not been refinished. It's original with receiver retaining 98% of its beautiful blue finish. The Fancy Grade Walnut stocks retain 100% original finish (X grade = Tiger Stripe grain). Please ask me for further...