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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).
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).
Excellent condition HK P30 SK LEM with mags (10 rd, 13 rd), SN-matching box, etc. PM for more photos or to FaceTime with the gun.
$550
$600 — first unqualified "I'll take it" in the thread gets it
I have additional mags (probably 5-6 and a mix of 10 and 13 rounders I believe) and a brand new...
This fantastic gun is doing too much time in the safe and deserves better! Original owner, all stock with <1k fired.
- Box and paperwork
- 3 ea. 15 round magazines
- Strong Night Sights
$900.00 + transfer, prefer FFL within PDX/ Metro but have some flex
No shipping or trades
-One owner in excellent condition with ~ 500 rounds fired
This is the Gen. 3 SF (short frame) version; Glock introduced this with a reduced grip circumference making it more manageable for folks with smaller hands.
-100% stock, box and factory accoutrements included
-2 ea. 13 round magazines (...
These are Colt takeoff handles that were removed from new rifles. Probably the best handles I have ever had condition wise. These are Milspec Height. I've had these in storage for years and they are mint!
$73 each or $68 shipped each if you buy both. Shipping will be via USPS priority...
I'll probably regret this, however, I can't bring myself to fire it, never mind carry it, it's too nice, so I'll let someone else deal with that dilemma. Knife complements it nicely.
$1400, no trades, no mags if it's staying in WA (I'd throw in 10rdrs but I don't have any, sorry)
Sound Loan...
Selling a surplus Astra NC-6 chambered in .38 special. Single/double action, Smith & Wesson style release, see pictures for finish condition. Functions perfectly.
For more information, https://www.classicfirearms.com/astra-nc6-revolver-38spl-6-shot/
WINCHESTER 1890 pump TAKE DOWN! NICE little rifle in 22 WRF! Very good overall original condition with all original bluing etc! This one too has been traveled and has smacked many a grey and ground squirrels over the years. Been in our family since 1930s. Really looks nice in person...
Ruger M77 Tang Safety 280 REM/7mm EXP REM! Excellent condition rifle in rare caliber! If you claim to be RUGER collector and dont have this grail rifle then your collection has fallen short! LOL!
100% original factory condition in excellent overall condition. Take a look at the pictures and...
Hello all,
Testing the waters here to see if there's a match out on this interweb. I bought the Hellcat new, and have fired it maybe 50-75 times. Like-new condition, and will come with everything it came with from the factory. There's a 3rd 15 round magazine to go with the 11/13 round units...
$425 Actually I'll do $400 $375 $350 (or shoot me a reasonable offer)
Sig sp2022 w/ two 15 rd magazines and two brand new 10 rd magazines. Pistol has small back strap on it with medium strap included.
The gun is in great shape. I bought it off gunbroker earlier this year and it appeared to...
I have 2 New Condition 1 Rolling Tactical Gun Cases.
Black one has a few bump marks from moving around but never used.
These hold 2/3 rifles. Depending on what you got.
Black one is great trunk size. FDE is a little big for most cars.
Would trade for a pistol or rifle light, plate carrier...
I have a very nice vintage Burris 3x-9x Fullfield scope (1" tube and 40mm front glass, standard cross-hair reticle) in very good condition for its age (these were manufactured in late 70s to early 80s in Colorado, USA). Optics is clear of any issues and external body is free of any dents...