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Nams- Roots of equations by numerical methodsRuchi Maurya
Bisection method. The simplest root-finding algorithm is the bisection method. ...
False position (regula falsi) ...
Interpolation. ...
Newton's method (and similar derivative-based methods) ...
Secant method. ...
Interpolation. ...
Inverse interpolation. ...
Brent's method.
In mathematics and computing, a root-finding algorithm is an algorithm, for finding values x such that f(x) = 0, for a given continuous function f from the real numbers to real numbers or from the complex numbers to the complex numbers. Such an x is called a root or zero of the function f. As, generally, the roots may not be described exactly, they are approximated as floating point numbers, or isolated in small intervals (or disks for complex roots), an interval or disk output being equivalent to an approximate output together with an error bound.
Solving an equation f(x) = g(x) is the same as finding the roots of the function f – g. Thus root-finding algorithms allows solving any equation.
Numerical root-finding methods use iteration, producing a sequence of numbers that hopefully converge towards the root as a limit. They require one or more initial guesses of the root as starting values, then each iteration of the algorithm produces a successively more accurate approximation to the root. Since the iteration must be stopped at some point these methods produce an approximation to the root, not an exact solution. Many methods compute subsequent values by evaluating an auxiliary function on the preceding values. The limit is thus a fixed point of the auxiliary function, which is chosen for having the roots of the original equation as fixed points.
The behaviour of root-finding algorithms is studied in numerical analysis. Algorithms perform best when they take advantage of known characteristics of the given function, so different algorithms are used to solve different types of equations. Desirable characteristics include a rapid rate of convergence, ability to separate close roots, robustness against failures of differentiability, and low propagation rate of rounding errors.
Nams- Roots of equations by numerical methodsRuchi Maurya
Bisection method. The simplest root-finding algorithm is the bisection method. ...
False position (regula falsi) ...
Interpolation. ...
Newton's method (and similar derivative-based methods) ...
Secant method. ...
Interpolation. ...
Inverse interpolation. ...
Brent's method.
In mathematics and computing, a root-finding algorithm is an algorithm, for finding values x such that f(x) = 0, for a given continuous function f from the real numbers to real numbers or from the complex numbers to the complex numbers. Such an x is called a root or zero of the function f. As, generally, the roots may not be described exactly, they are approximated as floating point numbers, or isolated in small intervals (or disks for complex roots), an interval or disk output being equivalent to an approximate output together with an error bound.
Solving an equation f(x) = g(x) is the same as finding the roots of the function f – g. Thus root-finding algorithms allows solving any equation.
Numerical root-finding methods use iteration, producing a sequence of numbers that hopefully converge towards the root as a limit. They require one or more initial guesses of the root as starting values, then each iteration of the algorithm produces a successively more accurate approximation to the root. Since the iteration must be stopped at some point these methods produce an approximation to the root, not an exact solution. Many methods compute subsequent values by evaluating an auxiliary function on the preceding values. The limit is thus a fixed point of the auxiliary function, which is chosen for having the roots of the original equation as fixed points.
The behaviour of root-finding algorithms is studied in numerical analysis. Algorithms perform best when they take advantage of known characteristics of the given function, so different algorithms are used to solve different types of equations. Desirable characteristics include a rapid rate of convergence, ability to separate close roots, robustness against failures of differentiability, and low propagation rate of rounding errors.
Numerical Methods and Applied Statistics Paper (RTU VI Semester)FellowBuddy.com
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Numerical Methods and Applied Statistics Paper (RTU VI Semester)FellowBuddy.com
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
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JLK Chapter 5 – Methods and ModularityDRAFT January 2015 Edition.docxvrickens
JLK Chapter 5 – Methods and ModularityDRAFT January 2015 Edition pg. 25
An Introduction to
Computer Science with Java, Python and C++
Community College of Philadelphia edition
Copyright 2017 by C.W. Herbert, all rights reserved.
Last edited October 8, 28, 2019 by C. W. Herbert
This document is a draft of a chapter from An Introduction to Computer Science with Java, Python and C++, written by Charles Herbert. It is available free of charge for students in Computer Science courses at Community College of Philadelphia during the Fall 2019 semester. It may not be reproduced or distributed for any other purposes without proper prior permission.
Please report any typos, other errors, or suggestions for improving the text to [email protected]
Chapter 5 – Python Functions and Modular Programming
Contents
Lesson 5.1User Created Functions in Python2
Python Function Parameters2
Value returning functions3
Example – Methods and Parameter Passing5
9
Lesson 5.2Top-Down Design and Modular Development10
Chapter Exercises13
User Created Functions in Python
So far we have only created software with one continuous Python script. We have used functions from other python modules, such as the square root method from the math class math.sqrt(n). Now we will begin to create our own functions of our own.
A Python function is a block of code that can be used to perform a specific task within a larger computer program. It can be called as needed from other Python software. Most programming languages have similar features, such as methods in Java or subroutines in system software.
The code for user-defined functions in Python is contained in a function definition. A Python function definition is a software unit with a header and a block of Python statements. The header starts with the keyword def followed by the name of the function, then a set parenthesis with any parameters for the function. A colon is used after the parentheses to indicate a block of code follows, just as with the if and while statements. The block of code to be included within the function is indented.
Here is an example of a Python function:
# firstFunction.py
# first demonstration of the use of a function for CSCI 111
# last edited 10/08/2o19 by C. Herbert
function
definition
def myFunction():
print ( "This line being printed by the function MyFunction.\n")
# end myFunction()
### main program ###
function used by the main part of the script
print("Beginning\n")
myFunction()
print("End\n")
# end main program
Functions can used for code that will be repeated within a program, or for modular development, in which long programs are broken into parts and the parts are developed independently. The parts can be developed as Python functions, then integrated to work together by being called from other software.
Python Function Parameters
Data can be passed to a Python function as a parameter of the function. Function parameters are variables listed in parentheses foll ...
The first lecture of the ACM Aleppo CPC training. The local contest of ICPC. This lecture will help you get started in programming contests word with the lower bound techniques. The lectures focus on the C++ programming language and the STL library to solve programming problems.
Algorithms Lecture 1: Introduction to AlgorithmsMohamed Loey
We will discuss the following: Algorithms, Time Complexity & Space Complexity, Algorithm vs Pseudo code, Some Algorithm Types, Programming Languages, Python, Anaconda.
Understand and interpret concept the loop statements and give some examples. • Students can design programs involving loop statements. • Gain knowledge and understanding of function of the loops inside the program. • Students can compare between loop statements , Iteration. , Loop structure, While - Do while, For - Loop control statement (start, end and step).
, Control all loops by break & continue statements, Infinite loop,Explain the different loops available in language with examples, Differ between loop control statement and the infinite loop , by Eng.&Educator Osama Ghandour
LESSON 3B. FOCUS: FOR LOOPS, NESTED LOOPS, TASKS AND CHALLENGES.
Introduction to, with examples, For loops. Challenges and tasks included with solutions (predict the output). Compare ‘while’ and ‘for’ loops. Use the break statement and explore how it works in different scenarios. Learn about Nested Loops. Learn about the need for initialisation (set starting value). Create your own for loops. Create the beginnings of an arithmetic quiz using a random function and for loops. Big ideas discussion: Is the universe digital. A program? Introducing Gottfried Leibniz and Konrad Zuse. Includes a suggested videos, ‘Big ideas’ discussion, and HW/research projects section.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.