Question
In: Advanced Math
Use Muller's method to find a solution in [0.1, 1] accurate to within 600x^4−550x^3+200x^2−20x−1=0. Explain how...
Use Muller's method to find a solution in [0.1, 1] accurate to within 600x^4−550x^3+200x^2−20x−1=0. Explain how the algorithm works.
Solutions
Expert Solution
IF YOU HAVE ANY DOUBTS COMMENT BELOW I WILL BE TTHERE TO HELP YOU..ALL THE BEST..
AS FOR GIVEN DATA...
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define ESP 0.001
#define F(x) (x)*(x)*(x) + 2*(x)*(x) + 10*(x) - 20
void main()
{
double x1,x2,x3,x4_1,x4_2,fx1,fx2,fx3,
h1,h2,h3_1,h3_2,h4,D,d1,d2,a1,a2,a0;
int i=1;
clrscr();
printf("\nEnter the value of x1: ");
scanf("%lf",&x1);
printf("\nEnter the value of x2: ");
scanf("%lf",&x2);
printf("\nEnter the value of x3: ");
scanf("%lf",&x3);
fx1 = F(x1);
printf("\n\n f(x1) = %lf",fx1);
getch();
fx2 = F(x2);
printf("\n\n f(x2) = %lf",fx2);
getch();
fx3 = a0 = F(x3);
printf("\n\n f(x3) = %lf",fx3);
getch();
h1 = x1-x3;
h2 = x2-x3;
d1 = fx1-fx3;
d2 = fx2-fx3;
D = h1*h2*(h1-h2);
a1 = (d2*h1*h1 - d1*h2*h2)/D;
a2 = (d1*h2 - d2*h1)/D;
h3_1 = -((2*a0)/(a1 + sqrt(fabs(a1*a1 - (4*a2*a0)))));
h3_2 = -((2*a0)/(a1 - sqrt(fabs(a1*a1 - (4*a2*a0)))));
if( (a1 + sqrt(fabs(a1*a1 - (4*a2*a0)))) >
((a1 - sqrt(fabs(a1*a1 - (4*a2*a0))))) )
{
h4 = h3_1;
}
else
{
h4 = h3_2;
}
x4_1 = x3 + h4;
printf("\n\n\n x4 = %lf \n",x4_1);
x1=x2;
x2=x3;
x3=x4_1;
printf("\n\nx1 = %lf",x1);
printf("\n\nx2 = %lf",x2);
printf("\n\nx3 = %lf",x3);
getch();
do
{
fx1 = F(x1);
fx2 = F(x2);
fx3 = a0 = F(x3);
h1 = x1-x3;
h2 = x2-x3;
d1 = fx1-fx3;
d2 = fx2-fx3;
D = h1*h2*(h1-h2);
a1 = (d2*h1*h1 - d1*h2*h2)/D;
a2 = (d1*h2 - d2*h1)/D;
h3_1 = -((2*a0)/(a1 + sqrt(fabs(a1*a1 - (4*a2*a0)))));
h3_2 = -((2*a0)/(a1 - sqrt(fabs(a1*a1 - (4*a2*a0)))));
if( (a1 + sqrt(fabs(a1*a1 - (4*a2*a0)))) >
(a1 - sqrt(fabs(a1*a1 - (4*a2*a0)))) )
{
h4 = h3_1;
}
else
{
h4 = h3_2;
}
x4_2 = x3 + h4;
printf("\n\n\n x4 = %lf \n",x4_2);
getch();
if(fabs(x4_1 - x4_2) < ESP)
{
printf("\n\nREAL ROOT = %.3lf",x4_2);
i=0;
}
else
{
x4_1=x4_2;
x1=x2;
x2=x3;
x3=x4_1;
printf("\n\nx1 = %lf",x1);
printf("\n\nx2 = %lf",x2);
printf("\n\nx3 = %lf",x3);
}
}while(i!=0);
getch();
}
/*
____________________________
OUT PUT
____________________________
Enter the value of x1: 0
Enter the value of x2: 1
Enter the value of x3: 2
f(x1) = -20.000000
f(x2) = -7.000000
f(x3) = 16.000000
x4 = 1.354066
x1 = 1.000000
x2 = 2.000000
x3 = 1.354066
x4 = 1.368647
x1 = 2.000000
x2 = 1.354066
x3 = 1.368647
x4 = 1.368808
REAL ROOT = 1.369
*/
Code for MULLER'S METHOD in C Programming
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define ESP 0.001
#define F(x) (x)*(x)*(x) + 2*(x)*(x) + 10*(x) - 20
void main()
{
double x1,x2,x3,x4_1,x4_2,fx1,fx2,fx3,
h1,h2,h3_1,h3_2,h4,D,d1,d2,a1,a2,a0;
int i=1;
clrscr();
printf("\nEnter the value of x1: ");
scanf("%lf",&x1);
printf("\nEnter the value of x2: ");
scanf("%lf",&x2);
printf("\nEnter the value of x3: ");
scanf("%lf",&x3);
fx1 = F(x1);
printf("\n\n f(x1) = %lf",fx1);
getch();
fx2 = F(x2);
printf("\n\n f(x2) = %lf",fx2);
getch();
fx3 = a0 = F(x3);
printf("\n\n f(x3) = %lf",fx3);
getch();
h1 = x1-x3;
h2 = x2-x3;
d1 = fx1-fx3;
d2 = fx2-fx3;
D = h1*h2*(h1-h2);
a1 = (d2*h1*h1 - d1*h2*h2)/D;
a2 = (d1*h2 - d2*h1)/D;
h3_1 = -((2*a0)/(a1 + sqrt(fabs(a1*a1 - (4*a2*a0)))));
h3_2 = -((2*a0)/(a1 - sqrt(fabs(a1*a1 - (4*a2*a0)))));
if( (a1 + sqrt(fabs(a1*a1 - (4*a2*a0)))) >
((a1 - sqrt(fabs(a1*a1 - (4*a2*a0))))) )
{
h4 = h3_1;
}
else
{
h4 = h3_2;
}
x4_1 = x3 + h4;
printf("\n\n\n x4 = %lf \n",x4_1);
x1=x2;
x2=x3;
x3=x4_1;
printf("\n\nx1 = %lf",x1);
printf("\n\nx2 = %lf",x2);
printf("\n\nx3 = %lf",x3);
getch();
do
{
fx1 = F(x1);
fx2 = F(x2);
fx3 = a0 = F(x3);
h1 = x1-x3;
h2 = x2-x3;
d1 = fx1-fx3;
d2 = fx2-fx3;
D = h1*h2*(h1-h2);
a1 = (d2*h1*h1 - d1*h2*h2)/D;
a2 = (d1*h2 - d2*h1)/D;
h3_1 = -((2*a0)/(a1 + sqrt(fabs(a1*a1 - (4*a2*a0)))));
h3_2 = -((2*a0)/(a1 - sqrt(fabs(a1*a1 - (4*a2*a0)))));
if( (a1 + sqrt(fabs(a1*a1 - (4*a2*a0)))) >
(a1 - sqrt(fabs(a1*a1 - (4*a2*a0)))) )
{
h4 = h3_1;
}
else
{
h4 = h3_2;
}
x4_2 = x3 + h4;
printf("\n\n\n x4 = %lf \n",x4_2);
getch();
if(fabs(x4_1 - x4_2) < ESP)
{
printf("\n\nREAL ROOT = %.3lf",x4_2);
i=0;
}
else
{
x4_1=x4_2;
x1=x2;
x2=x3;
x3=x4_1;
printf("\n\nx1 = %lf",x1);
printf("\n\nx2 = %lf",x2);
printf("\n\nx3 = %lf",x3);
}
}while(i!=0);
getch();
}
/*
____________________________
OUT PUT
____________________________
Enter the value of x1: 0
Enter the value of x2: 1
Enter the value of x3: 2
f(x1) = -20.000000
f(x2) = -7.000000
f(x3) = 16.000000
x4 = 1.354066
x1 = 1.000000
x2 = 2.000000
x3 = 1.354066
x4 = 1.368647
x1 = 2.000000
x2 = 1.354066
x3 = 1.368647
x4 = 1.368808
REAL ROOT = 1.369
*/
HOPE IT HELPS YOU
RATE THUMBSUP IT HELPS ME ALOT
THANKS
Colby Messinger answered 2 years agoRelated Solutions
Numerical Analysis: Use Muller's method to find a solution in [0.1, 1] accurate to within 600x^4−550x^3+200x^2−20x−1=0....
Numerical Analysis:
Use Muller's method to find a solution in [0.1, 1] accurate to
within 600x^4−550x^3+200x^2−20x−1=0. Explain how the algorithm
works.
Please show table with all values, not just the final root
value.
1. Use the Laplace transform to solve the initial value problem. ?"+4?′+3?=1−?(?−2)−?(?−4)+?(?−6), ?(0)=0, ?′(0)=0 2. Use...
1. Use the Laplace transform to solve the initial value
problem.
?"+4?′+3?=1−?(?−2)−?(?−4)+?(?−6), ?(0)=0, ?′(0)=0
2. Use the Laplace transform to solve the initial value
problem.
?"+4?=?(?), ?(0)=1, ?′(0)=−1
= { 1, ? < 1
where ?(?) = {0, ? > 1.
Consider the following data: x -4 -3 -2 -1 0 P(X=x) 0.2 0.1 0.2 0.1 0.4...
Consider the following data:
x
-4
-3
-2
-1
0
P(X=x)
0.2
0.1
0.2
0.1
0.4
Step 2 of 5 : Find the variance. Round your answer to one
decimal place.
Step 3 of 5 : Find the standard deviation. Round your answer to
one decimal place.
A= 1 2 4 0 1 -2 -1 0 1 2 0 3 8 1 4...
A=
1
2
4
0
1
-2
-1
0
1
2
0
3
8
1
4
. Let W denote the row space for A.
(a) Find an orthonormal basis for W and for W⊥.
(b) Compute projW⊥(1 1 1 1 1 ).
x P(x) 0 0.15 1 0.1 2 0.3 3 0.45 Find the mean of this probability...
x
P(x)
0
0.15
1
0.1
2
0.3
3
0.45
Find the mean of this probability distribution. Round your answer
to one decimal place.
2
x
P(x)
0
0.05
1
0.15
2
0.25
3
0.55
Find the standard deviation of this probability distribution. Give
your answer to at least 2 decimal places
3
2.36 Is it worth it?: Andy is always looking
for ways to make money fast. Lately, he has been trying to make
money by gambling. Here is...
exampleInput.txt 1 2 3 0 2 3 4 0 1 3 5 0 1 2 6...
exampleInput.txt
1 2 3
0 2 3 4
0 1 3 5
0 1 2 6
1 5 6 8
2 4 6 7
3 4 5 9 10
5 8 9
4 7 9
6 7 8
6
How can I detect when 'cin' starts reading from a new line. The
amount of numbers in each row is unknown. I need them in type 'int'
to use the data.
Assuming that x>0, use the method of reduction of order to find a second solution to...
Assuming that x>0, use the method of reduction of order to
find a second solution to
x^2y''−3xy'+4y=0
Given y1(x)=x^2
Let y′=y(4−ty) and y(0)=0.85. Use Euler's method to find approximate values of the solution of the...
Let y′=y(4−ty) and y(0)=0.85.
Use Euler's method to find approximate values of the solution of
the given initial value problem at t=0.5,1,1.5,2,2.5, and 3 with
h=0.05.
Carry out all calculations exactly and round the final answers
to six decimal places.
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4.
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2.
3. 4.
A.)MEAN –
B.)MEDIAN -
C.)MODE -
D.)STANDARD DEVIATION –
E.)5 NUMBER SUMMARY –
F.)BOX AND WHISKERS PLOT –
G.) OUTLIERS-
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2. 3. 4.
0. 0. 0. 0.0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 2. 2. 2.
3. 4.
A.)5 NUMBER SUMMARY –
B.)BOX AND WHISKERS PLOT –
C.) OUTLIERS-
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Mobile and wireless devices are being increasingly used in the Business Administration and Management Industry. write...
- What are the options that might be considered in relation to introducing flexible work practices? What...
- Question 2 : Aggregate Scores: Write a program that opens 2 files, quiz.txt, and hw.txt. The...
- Define the term symbiosis specifically as it applies in a biological context. Compare and contrast parasitism,...
- A research team conducted a study showing that approximately 20% of all businessmen who wear ties...
- Research the internet for companies that have executed data science projects. Pick one company and describe...
- Explain two theories or frameworks for understanding how Western Europe emerged out of 1,000 years of...
ADVERTISEMENT