False Point Method / Regula falsi method
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This lecture contains False Point Method working rule, Graphical representation, Example, Pros and cons of this method and a Matlab Code.
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This document describes the False Position Method for finding the roots of equations. The method uses linear interpolation to estimate the root between two initial guesses that bracket it. It improves on the bisection method by choosing a "false position" where the line between the guesses crosses the x-axis, rather than the midpoint. The false position formula is derived using similar triangles. An example applying the method to find a root of x^3 - 2x - 3 = 0 is shown. The merits of the false position method are faster convergence compared to bisection, while the demirits are possible non-monotonic convergence and lack of precision guarantee.
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The document discusses numerical methods for finding roots of functions. It introduces the bisection method for finding a root of a continuous function f(x) within a given interval [a,b] where f(a) and f(b) have opposite signs. The method bisects the interval into two subintervals and recursively narrows in on the root by testing the sign of f(x) at the midpoint of each subinterval. An example applies the bisection method to find a root of the function f(x)=x^3-x-1 between 1 and 2.
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This document discusses methods for solving algebraic and transcendental equations. It begins by defining key terms like roots, simple roots, and multiple roots. It then distinguishes between direct and iterative methods. Direct methods provide exact solutions, while iterative methods use successive approximations that converge to the exact root. The document focuses on iterative methods and describes how to obtain initial approximations, including using Descartes' rule of signs and the intermediate value theorem. It also discusses criteria for terminating iterations. One iterative method described in detail is the method of false position, which approximates the curve defined by the equation as a straight line between two points.
Numarical values highlighted
This document discusses methods for solving algebraic and transcendental equations. It begins by defining key terms like roots, simple roots, and multiple roots. It then distinguishes between direct and iterative methods. Direct methods provide exact solutions, while iterative methods use successive approximations that converge to the exact root. The document focuses on iterative methods and describes how to obtain initial approximations, including using Descartes' rule of signs and the intermediate value theorem. It also discusses criteria for terminating iterations. One iterative method described in detail is the method of false position, which approximates the curve defined by the equation as a straight line between two points.
Similar a False Point Method / Regula falsi method (20)
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Quadraticfunctionpresentation 100127142417-phpapp02
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Gas agency management system project report.pdf
The project entitled "Gas Agency" is done to make the manual process easier by making it a computerized system for billing and maintaining stock. The Gas Agencies get the order request through phone calls or by personal from their customers and deliver the gas cylinders to their address based on their demand and previous delivery date. This process is made computerized and the customer's name, address and stock details are stored in a database. Based on this the billing for a customer is made simple and easier, since a customer order for gas can be accepted only after completing a certain period from the previous delivery. This can be calculated and billed easily through this. There are two types of delivery like domestic purpose use delivery and commercial purpose use delivery. The bill rate and capacity differs for both. This can be easily maintained and charged accordingly.
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一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
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As digital technology becomes more deeply embedded in power systems, protecting the communication
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Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
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at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
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Mechatronics material . Mechanical engineering
Mechatronics is a multidisciplinary field that refers to the skill sets needed in the contemporary, advanced automated manufacturing industry. At the intersection of mechanics, electronics, and computing, mechatronics specialists create simpler, smarter systems. Mechatronics is an essential foundation for the expected growth in automation and manufacturing.
Mechatronics deals with robotics, control systems, and electro-mechanical systems.
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Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
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The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
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* Registration is currently open *
Call for Research Papers!!!
Free – Extended Paper will be published as free of cost.
3rd International Conference on Artificial Intelligence Advances (AIAD 2024)
July 13 ~ 14, 2024, Virtual Conference
Webpage URL: https://aiad2024.org/index
Submission Deadline: June 22, 2024
Submission System URL:
https://aiad2024.org/submission/index.php
Contact Us:
Here's where you can reach us : aiad@aiad2024.org (or) aiadconference@yahoo.com
WikiCFP URL: http://wikicfp.com/cfp/servlet/event.showcfp?eventid=180509©ownerid=171656
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False Point Method / Regula falsi method
- 1. Numerical Computing Lecture # 11 Regula Falsi Method By Nasima Akhtar
- 2. Working Rule • The Regula–Falsi Method is a numerical method for estimating the roots of a polynomial f(x). A value x replaces the midpoint in the Bisection Method and serves as the new approximation of a root of f(x). The objective is to make convergence faster. Assume that f(x) is continuous. • This method also known as CHORD METHOD ,, LINEAR INTERPOLATION and method is one of the bracketing methods and based on intermediate value theorem
- 4. Derivation • Equation Of line gives us: • 𝑦 − 𝑦1 𝑥 − 𝑥1 = 𝑦2− 𝑦1 𝑥2− 𝑥1 • 𝑦 − 𝑦1 = 𝑦2− 𝑦1 𝑥2− 𝑥1 (𝑥 − 𝑥1) • (𝑥1, 𝑦1)=(a,f(a)), (𝑥2, 𝑦2)=(b,f(b)), (𝑥 , 𝑦 )=(𝑥0, 𝑦0) • y- f(a) = f(b)−f(a) b− 𝑎 (𝑥 −a) • 0- f(a) = f(b)−f(a) b− 𝑎 (𝑥 −a) at x-axis y=0 • 0- f(a) = f(b)−f(a) b− 𝑎 (𝑥 −a) • (b− 𝑎)(− f(a) ) f(b)−f(a) =x-a • a + (b− 𝑎)(− f(a) ) f(b)−f(a) =x • 𝑎(f(b)−f(a))+(b− 𝑎)(− f(a) ) f(b)−f(a) =x ` • 𝑎(f(b))−a(f(a))−b(f(a) )+a(f(a) ) f(b)−f(a) =x ` • 𝑎(f(b)) −b(f(a) ) f(b)−f(a) =x ` • X= 𝑎(f(b)) −b(f(a) ) f(b)−f(a) `
- 5. Algorithm 1.Find points a and b such that a < b and f(a) * f(b) < 0. 2.Take the interval [a, b] and determine the next value of x1. 3.If f(x1) = 0 then x1 is an exact root, else if f(x1) * f(b) < 0 then let a = x1, else if f(a) * f(x1) < 0 then let b = x1. 4.Repeat steps 2 & 3 until f(xi) = 0 or |f(xi)| tolerance
- 6. Example Numerical • Find Approximate root using Regula Falsi method of the equation 𝑥3-4x+1 Putting values in x= 𝑎(f(b)) −b(f(a) ) f(b)−f(a) ` X F(x) a=0 1 b=1 -2 𝑥0=0.3333 F(𝑥0)= -0.2963 𝑥1=0.25714 F(𝑥1)= -0.0115 𝑥2=0.2542 F(𝑥2)= -0.0003 𝑥3=0.2541 F(𝑥3)= -0.00001 𝑥4=0.2541
- 7. Pros and Cons Advantages • 1. It always converges. • 2. It does not require the derivative. • 3. It is a quick method. Disadvantages • 1. One of the interval definitions can get stuck. • 2. It may slowdown in unfavourable situations.
- 8. Matlab Code f=@(x)(x^3+3*x-5); x1=1; x2 = 2; i = 0; val = f(x2); val1 = f(x1); if val*val1 >= 0 i = 99; end while i <= 4 val = f(x2); val1 = f(x1);24 temp = x2 - x1; temp1 = val - val1; nVal = temp/temp1; nVal = nVal * val; nVal = x2 - nVal; if (f(x2)*nVal <= 0) x1 = x2; x2 = nVal; else if (f(x1)*nVal <= 0) x2 = nVal; end end i = i+1; end fprintf('Point is %fn',x2) fprintf('At This Point Value is %fn',f(x2))