A textbook of Computer Based Numerical and Statiscal Techniques part 59 ppsx
A textbook of Computer Based Numerical and Statiscal Techniques part 59 ppsx
... < 0)
572
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
13.9 PROGRAMMING FOR NEWTON RAPHSON METHOD
(1) Find the Real Root of the Given Equation x
2
= 12
//program-netwon raphson
#include<conio.h>
#include<stdio.h>
#include<math.h>
float ... 13.11
ALGORITHM FOR NEWTON’S FORWARD INTERPOLATION
METHOD
Step 1. Start of the program to interpolate the given d...
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
... 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 the computed value of g is ... 4008 and 30.4647 + 0.0639 =
30.5286.
Example 12. Find the product of 346.1 and 865.2 and state how many figures of the result are
trustworthy, given that the numbers are corr...
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 div...
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 ... hD hD
hD
116
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 14. Evaluate the following:
I. ∆
2
(cos 2x)
II. ∆
2
(3e
x
)
III. ∆ tan
–1
x
IV. ∆(x + cos x)
the inte...
A textbook of Computer Based Numerical and Statiscal Techniques part 16 ppsx
... Suppose
for n + 1 equidistant argument values x = a, a + h, a + 2h, , a + nh, are given.
140
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Sol. For the given data, difference table is:
∆∆ ∆ ∆
−
−
−
−
−
−
∆
∆
∆∆
∆
∆∆
∆
∆
234
3
2
2
3
3
43
2
54
3
54
2
65
6
7
01
2
11 ... 0f−+×−×+=
138
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
i.e., 4f(3) = 124
i.e., f(3)...
A textbook of Computer Based Numerical and Statiscal Techniques part 17 ppsx
... R.H.S.
3.9 FACTORIAL NOTATIONS
The product of n consecutive factors each at a constant difference and the first factor being x is
called a factorial function or a factorial polynomial of degree n and ... L.H.S.
150
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
CorCor
CorCor
Cor
ollary:ollary:
ollary:ollary:
ollary:
To show that,
()
n
n
x
∆
= n! h
n
and
1n+
∆...
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
... required polynomial.
Example 4. Value of f(x) are given at a, b, c. Show that the maximum is obtained by
x =
()
(
)
()
(
)
()
(
)
()
()
()
()
()
()
fa b c fb c a fc a b
fa b c fb...
A textbook of Computer Based Numerical and Statiscal Techniques part 26 ppsx
... differences
where as the difference defined earlier are called ordinary differences. Lagrange’s interpolation
formula has the disadvantage that if any other interpolation point were added, the interpolation
co-efficient ... (5)
244
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES
Example 10. Show that the sum of Lagrangian co-efficients is unity.
Sol. Let
()
x
∏
=
()
()
()
01...
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...