Chapter 4, Problem 54C

Question

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Answer 1

Expert Solution & Answer

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

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Answer 2

Expert Solution & Answer

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Expert Solution & Answer

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Expert Solution & Answer

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Answer 8

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Answer 9

Chapter 4, Problem 54C

Explanation of Solution

a.

Simple method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the simplePolynomial() method

public static double simplePolynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=0; i<a.length; i++)

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation.

a[2]× x × x is “2” operations.

a[3]× x × x × x is “3” operations

Answer 10

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Answer 11

Explanation of Solution

b.

Method to compute p(x) in O(n(logn)) time:

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the Polynomial() method

public static double Polynomial(double a[], double n)

{

//Declare the variable

double sum = 0;

int i=0;

//Loop executes until the length of array

while(i<a.length)

{

//Compute the polynomial of degree

sum = sum + a[i] * Math.pow(n, a.length - i - 1);

//Increment "i" by "1"

i = i++;

}

//Return the polynomial of degree

return sum;

}

Running time:

In the above code, the computation of polynomial of degree is given below:

For each and every array term,

a[0] is “0” operation.

a[1]× x is “1” operation

Answer 12

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Answer 13

Explanation of Solution

c.

Horner method to compute p(x):

Let us consider the “p(x)” polynomial of degree “n”.

The method to compute the polynomial of degree is given below:

//Define the HornerPolynomial() method

public static double HornerPolynomial(double a[],double n)

{

//Declare the variable

double sum = 0;

//Loop executes until the length of array

for(int i=1;i< a

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Check out a sample textbook solution

See solution

Answer 17

Chapter 4, Problem 1R Chapter 4, Problem 2R Chapter 4, Problem 3R Chapter 4, Problem 4R Chapter 4, Problem 5R Chapter 4, Problem 6R Chapter 4, Problem 7R Chapter 4, Problem 8R Chapter 4, Problem 9R Chapter 4, Problem 10R

Chapter 4, Problem 54C

Solution Summary: The author explains the simple method to compute the polynomial of degree.

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