Secant Method Secant Method Derivation Newtons Method 1
![Secant Method Secant Method](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-1.jpg)
![Secant Method – Derivation Newton’s Method (1) Approximate the derivative (2) Substituting Equation (2) Secant Method – Derivation Newton’s Method (1) Approximate the derivative (2) Substituting Equation (2)](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-2.jpg)
![Secant Method – Derivation The secant method can also be derived from geometry: The Secant Method – Derivation The secant method can also be derived from geometry: The](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-3.jpg)
![Algorithm for Secant Method 4 Algorithm for Secant Method 4](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-4.jpg)
![Step 1 Calculate the next estimate of the root from two initial guesses Find Step 1 Calculate the next estimate of the root from two initial guesses Find](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-5.jpg)
![Step 2 Find if the absolute relative approximate error is greater than the prespecified Step 2 Find if the absolute relative approximate error is greater than the prespecified](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-6.jpg)
![Example 1 You are working for ‘DOWN THE TOILET COMPANY’ that makes floats for Example 1 You are working for ‘DOWN THE TOILET COMPANY’ that makes floats for](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-7.jpg)
![Example 1 Cont. The equation that gives the depth x to which the ball Example 1 Cont. The equation that gives the depth x to which the ball](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-8.jpg)
![Example 1 Cont. Solution To aid in the understanding of how this method works Example 1 Cont. Solution To aid in the understanding of how this method works](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-9.jpg)
![Example 1 Cont. Let us assume the initial guesses of the root of as Example 1 Cont. Let us assume the initial guesses of the root of as](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-10.jpg)
![Example 1 Cont. The absolute relative approximate error Iteration 1 is at the end Example 1 Cont. The absolute relative approximate error Iteration 1 is at the end](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-11.jpg)
![Example 1 Cont. Figure 5 Graph of results of Iteration 1. 12 Example 1 Cont. Figure 5 Graph of results of Iteration 1. 12](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-12.jpg)
![Example 1 Cont. Iteration 2 The estimate of the root is 13 Example 1 Cont. Iteration 2 The estimate of the root is 13](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-13.jpg)
![Example 1 Cont. The absolute relative approximate error Iteration 2 is at the end Example 1 Cont. The absolute relative approximate error Iteration 2 is at the end](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-14.jpg)
![Example 1 Cont. Figure 6 Graph of results of Iteration 2. 15 lmethods. eng. Example 1 Cont. Figure 6 Graph of results of Iteration 2. 15 lmethods. eng.](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-15.jpg)
![Example 1 Cont. Iteration 3 The estimate of the root is 16 Example 1 Cont. Iteration 3 The estimate of the root is 16](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-16.jpg)
![Example 1 Cont. The absolute relative approximate error Iteration 3 is at the end Example 1 Cont. The absolute relative approximate error Iteration 3 is at the end](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-17.jpg)
![Iteration #3 Figure 7 Graph of results of Iteration 3. 18 Iteration #3 Figure 7 Graph of results of Iteration 3. 18](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-18.jpg)
![Advantages n n 19 Converges fast, if it converges Requires two guesses that do Advantages n n 19 Converges fast, if it converges Requires two guesses that do](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-19.jpg)
![Drawbacks Division by zero 20 Drawbacks Division by zero 20](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-20.jpg)
![Drawbacks (continued) Root Jumping 21 Drawbacks (continued) Root Jumping 21](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-21.jpg)
- Slides: 21
![Secant Method Secant Method](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-1.jpg)
Secant Method
![Secant Method Derivation Newtons Method 1 Approximate the derivative 2 Substituting Equation 2 Secant Method – Derivation Newton’s Method (1) Approximate the derivative (2) Substituting Equation (2)](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-2.jpg)
Secant Method – Derivation Newton’s Method (1) Approximate the derivative (2) Substituting Equation (2) into Equation (1) gives the Secant method Figure 1 Geometrical illustration of the Newton-Raphson method. 2
![Secant Method Derivation The secant method can also be derived from geometry The Secant Method – Derivation The secant method can also be derived from geometry: The](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-3.jpg)
Secant Method – Derivation The secant method can also be derived from geometry: The Geometric Similar Triangles can be written as On rearranging, the secant method is given as Figure 2 Geometrical representation of the Secant method. 3
![Algorithm for Secant Method 4 Algorithm for Secant Method 4](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-4.jpg)
Algorithm for Secant Method 4
![Step 1 Calculate the next estimate of the root from two initial guesses Find Step 1 Calculate the next estimate of the root from two initial guesses Find](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-5.jpg)
Step 1 Calculate the next estimate of the root from two initial guesses Find the absolute relative approximate error 5
![Step 2 Find if the absolute relative approximate error is greater than the prespecified Step 2 Find if the absolute relative approximate error is greater than the prespecified](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-6.jpg)
Step 2 Find if the absolute relative approximate error is greater than the prespecified relative error tolerance. If so, go back to step 1, else stop the algorithm. Also check if the number of iterations has exceeded the maximum number of iterations. 6
![Example 1 You are working for DOWN THE TOILET COMPANY that makes floats for Example 1 You are working for ‘DOWN THE TOILET COMPANY’ that makes floats for](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-7.jpg)
Example 1 You are working for ‘DOWN THE TOILET COMPANY’ that makes floats for ABC commodes. The floating ball has a specific gravity of 0. 6 and has a radius of 5. 5 cm. You are asked to find the depth to which the ball is submerged when floating in water. Figure 3 Floating Ball Problem. 7
![Example 1 Cont The equation that gives the depth x to which the ball Example 1 Cont. The equation that gives the depth x to which the ball](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-8.jpg)
Example 1 Cont. The equation that gives the depth x to which the ball is submerged under water is given by Use the Secant method of finding roots of equations to find the depth x to which the ball is submerged under water. • Conduct three iterations to estimate the root of the above equation. • Find the absolute relative approximate error and the number of significant digits at least correct at the end of each iteration. 8
![Example 1 Cont Solution To aid in the understanding of how this method works Example 1 Cont. Solution To aid in the understanding of how this method works](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-9.jpg)
Example 1 Cont. Solution To aid in the understanding of how this method works to find the root of an equation, the graph of f(x) is shown to the right, where Figure 4 Graph of the function f(x). 9
![Example 1 Cont Let us assume the initial guesses of the root of as Example 1 Cont. Let us assume the initial guesses of the root of as](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-10.jpg)
Example 1 Cont. Let us assume the initial guesses of the root of as and Iteration 1 The estimate of the root is 10 lmethods. eng. usf. edu ht
![Example 1 Cont The absolute relative approximate error Iteration 1 is at the end Example 1 Cont. The absolute relative approximate error Iteration 1 is at the end](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-11.jpg)
Example 1 Cont. The absolute relative approximate error Iteration 1 is at the end of The number of significant digits at least correct is 0, as you need an absolute relative approximate error of 5% or less for one significant digits to be correct in your result. 11
![Example 1 Cont Figure 5 Graph of results of Iteration 1 12 Example 1 Cont. Figure 5 Graph of results of Iteration 1. 12](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-12.jpg)
Example 1 Cont. Figure 5 Graph of results of Iteration 1. 12
![Example 1 Cont Iteration 2 The estimate of the root is 13 Example 1 Cont. Iteration 2 The estimate of the root is 13](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-13.jpg)
Example 1 Cont. Iteration 2 The estimate of the root is 13
![Example 1 Cont The absolute relative approximate error Iteration 2 is at the end Example 1 Cont. The absolute relative approximate error Iteration 2 is at the end](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-14.jpg)
Example 1 Cont. The absolute relative approximate error Iteration 2 is at the end of The number of significant digits at least correct is 1, as you need an absolute relative approximate error of 5% or less. 14
![Example 1 Cont Figure 6 Graph of results of Iteration 2 15 lmethods eng Example 1 Cont. Figure 6 Graph of results of Iteration 2. 15 lmethods. eng.](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-15.jpg)
Example 1 Cont. Figure 6 Graph of results of Iteration 2. 15 lmethods. eng. usf. edu ht
![Example 1 Cont Iteration 3 The estimate of the root is 16 Example 1 Cont. Iteration 3 The estimate of the root is 16](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-16.jpg)
Example 1 Cont. Iteration 3 The estimate of the root is 16
![Example 1 Cont The absolute relative approximate error Iteration 3 is at the end Example 1 Cont. The absolute relative approximate error Iteration 3 is at the end](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-17.jpg)
Example 1 Cont. The absolute relative approximate error Iteration 3 is at the end of The number of significant digits at least correct is 5, as you need an absolute relative approximate error of 0. 5% or less. 17
![Iteration 3 Figure 7 Graph of results of Iteration 3 18 Iteration #3 Figure 7 Graph of results of Iteration 3. 18](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-18.jpg)
Iteration #3 Figure 7 Graph of results of Iteration 3. 18
![Advantages n n 19 Converges fast if it converges Requires two guesses that do Advantages n n 19 Converges fast, if it converges Requires two guesses that do](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-19.jpg)
Advantages n n 19 Converges fast, if it converges Requires two guesses that do not need to bracket the root
![Drawbacks Division by zero 20 Drawbacks Division by zero 20](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-20.jpg)
Drawbacks Division by zero 20
![Drawbacks continued Root Jumping 21 Drawbacks (continued) Root Jumping 21](https://slidetodoc.com/presentation_image_h/b97b6012c9349c6fb79ba2a00699d09c/image-21.jpg)
Drawbacks (continued) Root Jumping 21
Secant method
Leftmost derivation and rightmost derivation
Angle formed by tangent and secant
Secant method numerical method
Newtons method matlab
Dumas method formula
Slope deflection method definition
Newton raphson method
Secant method pseudocode
Cise flowchart
Bairstow algorithm
Secant method matlab
Secant method شرح
Secant method examples
Secant method nonlinear equations
Matematik
Newtons 3 rd law of motion
Inertia in soccer
Scope of personal selling
Describe newtons second law
Newton backward interpolation formula
Example of newton's first law