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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).
Winchester Model 50 20ga 2 3/4" Semi Auto in fantastic condition. Fixed modified choke. Gun shoots extremely pleasantly. Only point of modification appears to be previous owners inscribed initials into the wood under the handguard (only visible on disassembly). Gun uses a very interesting...
I have a great condition 1949 dated marlin 30-30 i am looking to sell. The rifles has maybe two little spots were there is slight surface rust. The stock is a little worn with a missing end cap were your palm sits. Other then that it is mechanically sound i personally have not shot it myself i...
Very good condition Badger mount, picked up a little spray paint from the upper this was mounted on. Overall very nice still, tan anodizing is in great condition. 1.7" height.
$250 no trades
For sale is my Microtech Amphibian Automatic with a blade date of January 2002. Black anodized handle with stonewashed blade. The bladesteel is 14-4CrMo, which is the standard steel for Microtechs of this era. The knife is in 100% unused condition with no wear or signs of use or handling...
Probably the wrong place to be posting a vintage film camera for trade, but here goes. Very cool little Voigtlander Vito C micro 35mm film camera. The kit is in mint condition. I bought from the original owner in Germany, and have had it for about 8 years. It's a mostly automatic rig, save...
First generation S&W striker fired pistol in 45 acp with three magazines. Comes with roughly 100 rounds of TulAmmo steel case, and 150 in hollow points between frangible and Federal HST
I bought this new. I've had surgery on one thumb and will have another next year. It's turned into a paperweight for me. My 70 year old hands will never be able to rack it I'm afraid. I've put approximately 300-400 rounds through it without any glitch at all. Always meticulously cleaned after...
A like new Sports Afield digital full size gun safe. I paid 650 and now its empty and ready to be sold. First 425 cash 97048 can back a truck right up to it.
Can be texted @ 971 203 6593 thankyou Chris
Found one of my grail guns and need to offload some stuff to foot the bill... have a like new glock 20 gen 4 as the title states. Pistol is in all but perfect condition and comes with factory box, papers,etc. (2) 15 round glock factory mags, (1) 15 round mag with a +2 extension, (2) boxes...
I have two Polish M44s in mint condition. One is dated 1953 and the other one is stamped 1955.
This package deal comes with two 880 round Albanian ammo crates and one 440 spam can - totaling 2200 rounds of 7.62x54R.
I want to sell all for $2,500.00.
Black finish with brown handgrip, minimally used. With carrying case, trigger lock, and HKS fast reload. $999. I have been the only owner of this pistol. Sale will take place in SafeFire Indoor shooting Range and Retail, 4857 NW Lake Road # 210, Camas, Wa 98607. I live in Camas.
1976 COLT GOLD CUP NATIONAL MATCH .45 ACP 70 SERIES, MINT CONDITION. BOX-PAPERS-TWO FACTORY 8 ROUND MAGS. NO TRADES AT THIS TIME, TRYING TO MAKE UP FOR A $$$ PURCHASE.
$1375 MEET AT TIGARD PAWN
Thanks for looking
I've decided to take the collection in a different direction so the Beretta is up for grabs.
Purchased brand new and has exactly 180 rounds fired. I don't normally keep track but for some reason I did on this one.
Absolutely 100% factory original in Like New condition
3 ea. 15 round magazines...
For sale is my Microtech Amphibian Automatic with a blade date of January 2002. Black anodized handle with stonewashed blade. The bladesteel is 14-4CrMo, which is the standard steel for Microtechs of this era. The knife is in 100% unused condition with no wear or signs of use or handling...
Here's a great opportunity to own a Used but Excellent Condition Ruger Red Label Shotgun. We have 2 for Sale. One is a 30" and the other is a 26" Over & Under 12 Gauge. These two are in stock and ready for a new home.
1. Ruger Red Label 30" 12 Gauge: $1799...
This EOTech 512.A65 holographic sight is in great shape and works perfectly.
Comes in the original plastic case with all paperwork, etc. as shown.
Front and back glass looks perfect with no scratches.
Mostly has just sat in my safe, so it's ready for a new, loving home. 👨👩👦
I am the...