Question

the book we use is numerical methods for engineers 7th edition

1. Use the Newton-Raphson Method to determine the roots for the following two problems with errors in the computed roots not more than 1.0% i) Solve parts (a) and (b) of problem 6.10 [textbook page 174] starting from Xi=0.15; ii)Solve problem 6.16 after re-writing (re-arranging) the nonlinear equations as u (x, y)-0, and v (r, y)-0 2. Use the method of Gauss Elimination to solve textbook Problem 9.11 [textbook page 2721 after writing the equations in a matrix form Ax-b. Also compute the determinant of the coefficient matrix and check the accuracy of your results x by substitution in matrix A x- b and computing the ratio of norms of vectors Ab and b (namely: ) ke 3. Determine the inverse of matrix A (given in textbook Problem 10.12 [textbook page 2981), and also determine its three matrix norms 4. Compute the condltion number for the matrix given in textbook Problenm 10.14. Also, check if the matrix is ill conditioned or not. Then, if it is ill conditioned specify the number of significant digits that will be lost due to ill-conditioning

Answer 1

Please post those problem, because we could not arrange all the books always.

For newton Raphson method use the recurrence relation x_(n+1) = x_(n) - df(x_(n))/f(x_(n)).

For Gauss elimination method use elementary row operation method to modify the coefficient matrix in an upper triangular matrix. Then find the values of the variables.