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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 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...
I want to sell my Leupold MK-4 8.5-24x50mm M1 LR/T Scope in MINT condition. I purchased this scope brand new 5 months ago (can provide receipt from MidwayUSA). The scope is in MINT condition and perfectly functional. This scope has second focal plane non-illuminated reticle. Scope comes in its...
Factory 26 (JIANSHE ARSONAL)Chinese spike bayonet SKS for sale. Matching numbers, imported into Washington State Originally. Well used, surplus condition, battle worn look without a dremel tool. Clean bore, good muzzle, cleaning rod, and another dust cover with a scope mount on it.
No trades...
SOLD. For sale is a Gen 3 Glock 23 in excellent condition. Round count is approximately 500 to 600. I've owned this since it was new.
WA residents: Price is $400 and it will include one 10rd magazine.
ID residents and where legal: Price is $450 and it will include one 10rd and six 13rd...
***SOLD***For sale is a Sig P229R .40 S&W in excellent condition. Can be easily converted to .357 Sig with barrel only (not included). Round count is approximately 600. I believe I bought this one back in about 2008.
WA residents: Price is $500, but unfortunately I cannot include the mags since...
FDE Badger mount 34mm .193 condition 1 like new. C.O.M.M
Trade for 35mm Badger Mounts, Consider other 35mm mounts
Trades
FSOT Silver/CASH/VENMO/PP willing to ship. Looking for but not limited to. EOTECH EXPSxx, HOLOSUN GREEN Enclosed or Primary arms Reticle, TIKKA T3X, Tremor 3 scopes, Colt...
Very good condition Badger mount, shows a little bit of wear on the very top of the mount. Overall very nice still. 1.7" height. No original box.
$250 shipped, no trades
1 owner Glock 34 Gen 3 with <500 rounds fired
Pistol remains in like new condition
100% stock
2 ea. 17 round magazines
$425.00 + transfer.
No shipping
Prefer local transfer within PDX/ Metro but have flexibility.
Photos are current 100% authentic. No scratches or wear, well maintained. Only light target loads fired. 4” Barrel, Blackhawk Holster included. Gunbroker has these selling at $1149 used. No trades
Mint condition, Winchester model, 94 in excellent shape no marks no dings no next it’s beautiful brand new has had less than 20 rounds fired through it and it’s entire life comes with 40rds of ammo
This is in excellent condition with drawers liners in all drawers with minimal wear to liners.
Top and bottom lock and keys are present.
Locking wheels.
Bottom is Red, 8 drawer.
26.75” w x 18” d x 40.25” tall from ground.
Top is Red, 10 drawer.
26” w 16” d 19.5” h
Serious inquiries only and...
I have been trying to get my wife into shooting for a while and she fell in love with shooting a friend's .22 revolver. This is a gun I could get excited about too as I LOVE the SP101 platform. I am interested in hearing about what is out there but our ability to make moves like this can be...
Up for grabs is a solid vintage spotting scope from tasco, model 3701 in camo. Includes the tripod, handle and factory covers for each end. This one has no issues, clear glass and has always been stored indoors. It’s as close to new as you’re going to get on one this old. Great scope!
Asking...
Ultimate range Staccato very fast shooting and super accurate. Gunsmith installed trigger and all receipts available. Have $5117.00 invested. Super clean excellent condition. Staccato quality and accessories at very low price.
I have a distressed silver Glock 17 gen 5 with 25 rounds through it. Turns out I don’t have a taste for glocks and want to go old school. I would love to trade it for a M44 Mosin nagant that’s in good condition
Hi all, I am selling my CZ Accushadow w/ slide cut for Sig Sauer Romeo 3 Max. Only 500 rounds shot. Love this Carry Optics pistol but selling to build a Limited Optics double stack 2011. CZ custom trigger, CZ custom barrel bushing, CZ custom trigger job, Slide cut by Springer Precision, Sig...