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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).
Pictures can be texted or emailed,Currently working on them what a P I T A...
Dimensions 47 1/2 tall X 73 longX29 Wide
I have this box that I bought in 2006, still pretty nice after 12 yrs of use...
Changed profession in 2018...
I have other boxes and room is needed...
Trade interests are...
Tavor SAR-B16 Bullpup Carbine 16.5" Barrel .223/5.56 NATO - $1549
Original owner, fewer than 100 rounds through this Tavor SAR-B16, chambered in 5.56NATO/.223 REM, as new condition. Includes 1 30-round magazine (uses standard AR-15 mags), original box, owner's kit, and lock. Cash only, no...
Sigsauer Romeo 05XDR red dot
After market Mesa Tactical rail system with vents
Spikes Tactical iron sites
Magpul forward grip
High tech custom concept muzzle break and stock
Oversized tube selector handle
High resolution followers with heavy duty springs
Keltec heavy duty shoulder saver
After...
I have a Vortex Gen 3 1-10 EBR-9 MRAD for sale it has seen good use and shows wear. It is functionally fine and the glass is still clear.
Would like to sell this as a package or will sell separate if I can get a buyer for the scope first.
$1850 + shipping for everything
OR
$1600 + shipping...
Included is holster and soft case if you want them. I got it a few years ago and never used it.
I am open to go down on that price make an offer in private message. I have a pretty good offer from a store but I know they are going to just sell it for what I'm asking
I am looking to buy a nice condition SxS shotgun. I would prefer a 20g but will consider 12g as well. I am not really looking for a new or newer gun. I would prefer a vintage/antique. Something with hammers would be nice but not required. Prefer something from around the turn of the century...
Comes with a Vortex 3.5-10x50mm scope. Excellent condition- the ultimate 6.5
Herters Rifles have BSA actions and Williams barrels. (24 inch barrel)
Very nice vintage rifle.
For Sale, NO trades