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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).
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...
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Up for sale a beautiful vintage generator. A true survivor with very little use. Only clear gas has been used across its life in an effort to mitigate gumming the carb. It's initial use case was as a power backup on a store register, so was only fired up to keep it working. After that, it's only...
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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...
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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