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MTH603 Current Midterm Paper Shared by Syeda Shehzadi, Spring 2014

   its today my paper:
    Q. Describe briefly the Jacobi’s method of solving linear equations? 2 marks
     Answer: In numerical linear algebra, the Jacobi method is an algorithm for determining the solutions of a diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jakob Jacobi.
    Given a square system of n linear equations:

    Perhaps the simplest iterative method for solving Ax = b is Jacobi`s method.


    Q. Write a formula for finding the value of p from Newton’s backward difference formula? 2 marks
    Answer:

    Q. Find the value of  from the following matrix by jacobi’s method 3 marks

    Q. Prove that  3 marks
    Solution:

    Q. Solve the following system of linear equations by Gauss-seidal iteration method up to two iterations and three decimal places 5 marks

Q. The sales for the last five years are given in the table below. Find Newton's backward difference tabl.
X(Years) 1974 1976 1978 1980 1982
Y(Sales in    lakhs) 40 43 48 52 57
                                             
 Solution:
X Y


1974 40


1976 43 3

1978 48 5 2
1980 52 5 0 -2
1982 57



 ...BEST of LUCK.....

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