Some definitions related Numerical Method
Significant figures: Significant
figure means how closely/significantly the result measured by the method we
applied.
Accuracy: Accuracy refers to how closely a
measured value agrees with the true value.
Differences betn Accuracy & Precision
Accuracy
|
Precision
|
i) Accuracy refers to how closely a
measured value agrees with the true value.
|
i) Precision refers to how closely measured values agree with each
other.
|
ii) Accuracy is a general concept.
|
ii) Precision is more of a mathematical concept.
|
iii) Accuracy means being correct and
true in every detail.
|
iii) Precision means being more exact and to the point in reference
to a certain standard.
|
iv) Accuracy may also refer to the
correctness of data.
|
iv) Precision can also refer to greater detail in description of an
object or concept.
|
Converging: The process of decreasing error
in every step is called converging.
Diverging: The process of increasing error
in every step is called diverging.
Limitation of floating-point:
(i)
There is a limited range of
quantity.
(ii)
There are only a finite number of
quantity that can be represented within the range.
(iii)
The interval betn
numbers ∆x increases as
the numbers grow in magnitude.
Trancket: Go to the minm value.
Rounding: Go to any of the nearest small
value.
Round-off error: A round-off
error is the difference betn the calculated approximation of a
number and its exact mathematical value.
[1 2 3] <-- is called Row matrix.
<--is called Column matrix.
{B} is the
notation of row & column matrix.
Square matrix: Where the number of column & row are equal.
<--Principle diagonal.
Diagonal matrix: The values of
principle diagonal are nonzero and other values are zero.
Identity matrix: If multiple
two matrix the result must be same as the 1st matrix.
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