Question: Write a Java program that creates a divided difference table from the given data in a text file and uses that to create the interpolating

Write a Java program that creates a divided difference table from the given data in a text file and uses that to create the interpolating polynomial. Print the polynomial in both the Newton's form and Lagrange's form. The sample output of your program for this input file (download the txt file here) should print out the divided difference table and the interpolating polynomial as shown below:

Write a Java program that creates a divided difference table from the

Interpolating polynomial is: 3 + 1/2(x-1) +1/3(x-1)(x-3/2) - 2(x-1)(x-3/2)x

Simplified polynomial is: -2x^3 + 5.334x^2 3.334x + 3

Your program should work on any data (at most 50 node points) and not just the above sample data.

Points distribution: 50% for printing out the correct divided difference table (data should be presented in fraction numbers), 25% for printing the correct polynomial in un-simplified form and 25% for printing the polynomial in simplified form.

Text file name is input.txt, and the content of the text file is

1 1.5 0 2

3 3.25 3 1.67

Chrome File Edit View History Bookmarks People Window Help A 100% E U.S Wed 1:07 a E B Assignments CS 301.0 (w x (G newton's divided differen ia x C Write A Program That creates x O NEWTON'S DIVIDED DIFFER x G read text file into array java x Hung c Secure https://blackboard.cpp.edi id 138839-1&content, ida 3333557-1&mod... Ar du E w. u/webapps/blackboard/content/listContent.jsp?course Apps school T Popcorn Time online warez-BB iMojado e The PirateBay ModMyl aFacebook YouTube a Amazon craigslist eBay Other Bookmarks f[] 1/2 3/2 13/4 1/3 1/6 5/3 2/3 5/3 Show Al X input.txt roj3.zip Chrome File Edit View History Bookmarks People Window Help A 100% E U.S Wed 1:07 a E B Assignments CS 301.0 (w x (G newton's divided differen ia x C Write A Program That creates x O NEWTON'S DIVIDED DIFFER x G read text file into array java x Hung c Secure https://blackboard.cpp.edi id 138839-1&content, ida 3333557-1&mod... Ar du E w. u/webapps/blackboard/content/listContent.jsp?course Apps school T Popcorn Time online warez-BB iMojado e The PirateBay ModMyl aFacebook YouTube a Amazon craigslist eBay Other Bookmarks f[] 1/2 3/2 13/4 1/3 1/6 5/3 2/3 5/3 Show Al X input.txt roj3.zip

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