A textbook of Computer Based Numerical and Statiscal Techniques part 12. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. | 96 COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES Now to obtain the values of bi and C we use the following procedure 1 6 18 24 16 -1 1 1 9 -1 1 3 1 3 6 Here from the table b3 b4 C1 -3 C2 C3 6 therefore after substituting the values of b and C in equations 1 and 2 we get A P - 3 Ap Aq - Aq Therefore the first approximation are given by p1 p0 Ap q1 q0 Aq 1 Second approximation Using p1 and q1 for second approximation then p2 p1 Ap and q2 q1 Aq. Now to obtain the values of b and C we use the following procedure ai 1 6 18 24 16 bi 1 Ci 1 After substituting the values of bi and C in equations 1 and 2 we get Ap ALGEBRAIC AND TRANSCENDENTAL EQUATION 97 Ap Aq Aq Therefore the second approximations are given by p2 p1 Ap q2 q1 Aq Third approximation Using p2 and q2 for third approximation then p3 p2 Ap and q3 q2 Aq. Now to obtain the values of b and C we use the following procedure a 1 -6 18 -24 16 ti 1 Ci 1 After substituting the values of b and C in equations 1 and Ap Ap - Aq - Aq Therefore the third approximation are given by p3 p2 Ap q3 q2 Aq 2 we get Thus we obtain p and q . Hence quadratic factor of the given equation is x2 - 0. Now if root of the quadratic factor is a .
