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23 Maths -- Numerical Computations

The characteristics of the computational method is accuracy rate of convergence numerical stability all of the above

The characteristics of the computational method is

  1. accuracy
  2. rate of convergence
  3. numerical stability
  4. all of the above


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More questions on Numerical Computations

Applying the method of successive bisection find square root of 3 within the two places of decimal in (1,2)

Using bisection method, find the root of the equation f(x)=x2 -6logx-3=0(2<=x<=3)'correct to 4 decimal places with an accuracy of 10 -2 .

Here, f(x)=x2 -6 logx-3=0

f(2)=4-6 log2-3=-0.806

f(3)=9-6 log3-3=3.1373

f(2).f(3)=-0.806*3.1373=-2.529422 which is negative.

Hence, the root lies between 2 and 3

c0 =(2+3)/2=2.5

f(2.5)=6.25-6 log 2.5-3=0.8623

Now

n
 a(-ve)
 b(+ve)
 cn
 f(cn)
0
 2
 3
 2.5
 0.8623
1
 2
 2.5
 2.25
 -0.050595
2
 2.25
 2.5
 2.375
 0.38664
3
 2.25
 2.375
 2.3125
 0.1631658
4
 2.25
 2.3125
 2.28125
 0.05506
5
 2.25
 2.28125
 2.265625
 0.001925

From the table,

f(2.265625)=0.001928<10-2

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