A textbook of Computer Based Numerical and Statiscal Techniques part 22 pps
A textbook of Computer Based Numerical and Statiscal Techniques part 22 pps
... 16.047
x
x
y
[Ans. 19.704]
202
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 4. Apply Stirling’s formula to find a polynomial of degree three which takes the following
values of x and y:
x
y ... 32.625 thousands
Hence, the population in 1936 is 32625 thousand.
196
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 5. If f(x) is a polynomial...
A textbook of Computer Based Numerical and Statiscal Techniques part 2 ppsx
... problems. A major
advantage for numerical technique is that a numerical answer can be obtained even when a
problem has no analytical solution. However, result from numerical analysis is an approximation,
in ... significant figures at each step of
computation. At each step of computations, retain at least one more significant figure
than that given in the data, perform the last...
A textbook of Computer Based Numerical and Statiscal Techniques part 3 ppsx
... 16(0.001) = 0.036
Also, Max. Relative Error =
=
0.036
0.009
4
(Because E
r(max)
=
δ
;
u
u
u = 4 at x = y = z = 1).
10
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Therefore, Relative Error, ... 3
Hence maximum percentage error (E
p
)
max
= 11.667%.
Example 26. How accurately should the length and time of vibration of a pendulum should be
measured in order that t...
A textbook of Computer Based Numerical and Statiscal Techniques part 5 ppsx
... roots of the equation, obtained by
x
1
=
2
22
44
and
22
bb ac bb ac
aa
−+ − −− −
=x
These are called closed form solution. Similar formulae are also available for cubic and
biquadratic polynomial ... 26
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
The basic operations specified by IEEE arithmetic are first and foremost addition, subtraction,
multiplication, and...
A textbook of Computer Based Numerical and Statiscal Techniques part 14 ppsx
... 122
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 22. Evaluate: ∆
n
[sin (ax + b)]
Sol. We know
f∆
(x) = f(x + h) – f (x) therefore
∆
sin (ax + b) = sin [a (x + h)+b] – sin)(ax ... 1, n) = (–1)
m
∆
m
1
n
124
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Therefore right hand side as
=
11 11
()()()()
22 22
11
()()
22
fx gx fx gx
gx...
A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx
... given a set of equidistant values of arguments and its corresponding value of f(x). Suppose
for n + 1 equidistant argument values x = a, a + h, a + 2h, , a + nh, are given.
140
COMPUTER BASED NUMERICAL ... 0f−+×−×+=
138
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
i.e., 4f(3) = 124
i.e., f(3) = 31
(function values are 3
n
type and this is not a pol...
A textbook of Computer Based Numerical and Statiscal Techniques part 17 ppsx
... abbx+−+=+−−
=
222 22
()(2)
a ab abbxbx x x−+ − + =α+β+γ
Comparing the coefficients of various powers of x we get
222
,2 ,
aab abb bα= − β= − γ=
Eliminating a and b from the above equations, we get
22
4
γ+αγ=β
This ... factorial notation.
Sol. Let,
()fx
=
2(2)
()
xx abxα+β +γ = +
where a and b are certain unknown constants.
Now,
(2)
()
abx+
=
()[(1)]abxabx++−
=
22
(...
A textbook of Computer Based Numerical and Statiscal Techniques part 25 ppsx
... interpolation formula.
Sol. We are given
()
:78910
:311 9
x
fx
226
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 1. Using Lagrange’s formula, find the value of
(i) y
x
if y
1
... Criminals for different age group are given below:
Age less than :25304050
Percentage of Criminals :52678494
Apply Lagrange’s formula to find the percentage of criminals under 35 year...
A textbook of Computer Based Numerical and Statiscal Techniques part 26 ppsx
... (5)
244
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 10. Show that the sum of Lagrangian co-efficients is unity.
Sol. Let
()
x
∏
=
()
()
()
01
n
xx xx xx
−− −
The reciprocal of ... 12.46
x
fx
[Ans. 8.337]
242
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 7. Find the value of x correct to one decimal place for which y = 7
Given
x:1 3 4...
A textbook of Computer Based Numerical and Statiscal Techniques part 29 ppsx
... co-efficients a
1
, a
2
a
n
will produce little
error for small x near zero. But probably substantial error near the ends of the interval
268
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
7. Apply ... approximation to a given function.
For evaluating a function f(x) on a computer it is generally more efficient of space and time
to have an analytic approxi...
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