Newton raphson
- 1. 11/5/2016 1
- 3. NEWTON-RAPHSON METHOD • Consider the solution of the one-dimensional • If 𝑥(0) is an initial estimate of the solution, and ∆𝑥(0) is a small deviation from the correct solution. Then we have math 11/5/2016 3
- 4. • Expanding by Taylor's series then we have • Assuming the error ∆𝑥(0) is very small, the higher-order terms can be neglected • because of • Then math NEWTON-RAPHSON METHOD 11/5/2016 4
- 5. • the first iteration will be math NEWTON-RAPHSON METHOD 11/5/2016 5
- 20. Example NEWTON-RAPHSON METHOD (n -1) x (n -1)) 11/5/2016 20
- 21. Example NEWTON-RAPHSON METHOD (n - 1) x (n - 1- m) 11/5/2016 21
- 22. Example NEWTON-RAPHSON METHOD ( n - 1 - m) x ( n - 1) 11/5/2016 22
- 23. Example NEWTON-RAPHSON METHOD ( n - 1 - m) x ( n - 1 - m) 11/5/2016 23