Secant method is mathematical Root finding method. Most of techniques like this method but it is useful and time managing strategy.
So, refer this method its is useful for root finding.
Secant method is mathematical Root finding method. Most of techniques like this method but it is useful and time managing strategy.
So, refer this method its is useful for root finding.
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.
Here we focuses on Fixed-Point Iterative Technique for solving nonlinear Equations in Numerical Analysis. It is one of the opened-iterative techniques for finding roots called Fixed-Point of Non-linear Equations.
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.
Here we focuses on Fixed-Point Iterative Technique for solving nonlinear Equations in Numerical Analysis. It is one of the opened-iterative techniques for finding roots called Fixed-Point of Non-linear Equations.
Contents of the presentation:
- ABOUT ME
- Bisection Method using C#
- False Position Method using C#
- Gauss Seidel Method using MATLAB
- Secant Mod Method using MATLAB
- Report on Numerical Errors
- Optimization using Golden-Section Algorithm with Application on MATLAB
This presentation is a part of Computer Oriented Numerical Method . Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques.
MATLAB DOCUMENTATION ON SOME OF THE MODULES
A.Generate videos in which a skeleton of a person doing the following Gestures.
1.Tilting his head to right and left
2.Tilting his hand to right and left
3.Walking
in matlab.
B. Write a MATLAB program that converts a decimal number to Roman number and vice versa.
C.Using EZ plot & anonymous functions plot the following:
· Y=Sqrt(X)
· Y= X^2
· Y=e^(-XY)
D.Take your picture and
· Show R, G, B channels along with RGB Image in same figure using sub figure.
· Convert into HSV( Hue, saturation and value) and show the H,S,V channels along with HSV image
E.Record your name pronounced by yourself. Try to display the signal(name) in a plot vs Time, using matlab.
F.Write a script to open a new figure and plot five circles, all centered at the origin and with increasing radii. Set the line width for each circle to something thick (at least 2 points), and use the colors from a 5-color jet colormap (jet).
G. NEWTON RAPHSON AND SECANT METHOD
H.Write any one of the program to do following things using file concept.
1.Create or Open a file
2. Read data from the file and write data to another file
3. Append some text to already existed file
4. Close the file
I.Write a function to perform following set operations
1.Union of A and B
2. Intersection of A and B
3. Complement of A and B
(Assume A= {1, 2, 3, 4, 5, 6}, B= {2, 4, 6})
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
CSCI 2033 Elementary Computational Linear Algebra(Spring 20.docxmydrynan
CSCI 2033: Elementary Computational Linear Algebra
(Spring 2020)
Assignment 1 (100 points)
Due date: February 21st, 2019 11:59pm
In this assignment, you will implement Matlab functions to perform row
operations, compute the RREF of a matrix, and use it to solve a real-world
problem that involves linear algebra, namely GPS localization.
For each function that you are asked to implement, you will need to complete
the corresponding .m file with the same name that is already provided to you in
the zip file. In the end, you will zip up all your complete .m files and upload the
zip file to the assignment submission page on Gradescope.
In this and future assignments, you may not use any of Matlab’s built-in
linear algebra functionality like rref, inv, or the linear solve function A\b,
except where explicitly permitted. However, you may use the high-level array
manipulation syntax like A(i,:) and [A,B]. See “Accessing Multiple Elements”
and “Concatenating Matrices” in the Matlab documentation for more informa-
tion. However, you are allowed to call a function you have implemented in this
assignment to use in the implementation of other functions for this assignment.
Note on plagiarism A submission with any indication of plagiarism will be
directly reported to University. Copying others’ solutions or letting another
person copy your solutions will be penalized equally. Protect your code!
1 Submission Guidelines
You will submit a zip file that contains the following .m files to Gradescope.
Your filename must be in this format: Firstname Lastname ID hw1 sol.zip
(please replace the name and ID accordingly). Failing to do so may result in
points lost.
• interchange.m
• scaling.m
• replacement.m
• my_rref.m
• gps2d.m
• gps3d.m
• solve.m
1
Ricardo
Ricardo
Ricardo
Ricardo
�
The code should be stand-alone. No credit will be given if the function does not
comply with the expected input and output.
Late submission policy: 25% o↵ up to 24 hours late; 50% o↵ up to 48 hours late;
No point for more than 48 hours late.
2 Elementary row operations (30 points)
As this may be your first experience with serious programming in Matlab,
we will ease into it by first writing some simple functions that perform the
elementary row operations on a matrix: interchange, scaling, and replacement.
In this exercise, complete the following files:
function B = interchange(A, i, j)
Input: a rectangular matrix A and two integers i and j.
Output: the matrix resulting from swapping rows i and j, i.e. performing the
row operation Ri $ Rj .
function B = scaling(A, i, s)
Input: a rectangular matrix A, an integer i, and a scalar s.
Output: the matrix resulting from multiplying all entries in row i by s, i.e. per-
forming the row operation Ri sRi.
function B = replacement(A, i, j, s)
Input: a rectangular matrix A, two integers i and j, and a scalar s.
Output: the matrix resulting from adding s times row j to row i, i.e. performing
the row operatio.
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.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. Bisection Method
The bisection method (sometimes called the midpoint method for equations) is a
method used to estimate the solution of an equation.
Like the Regula-Falsi Method (and others) we approach this problem by writing
the equation in the form f(x) = 0 for some function f(x). This reduces the problem
to finding a root for the function f(x).
Like the Regula-Falsi Method the Bisection Method also needs a closed interval
[a,b] for which the function f(x) is positive at one endpoint and negative at the
other. In other words f(x) must satisfy the condition f(a)⋅f(b) < 0. This means that
this algorithm can not be applied to find tangential roots.
There are several advantages that the Bisection method has over the Regula-
Falsi Method.
The number of steps required to estimate the root within the desired error
can be easily computed before the algorithm is applied. This gives a way to
compute how long the algorithm will compute. (Real-time applications)
The way that you get the next point is a much easier computation than how
you get the regula-falsi point (rfp).
3. Definition:-
• Given a closed interval [a,b] on which f changes sign, we
divide the interval in half and note that f must change
sign on either the right or the left half (or be zero at the
midpoint of [a,b].) We then replace [a,b] by the half-
interval on which f changes sign. This process is
repeated until the interval has total length less than
E(error) . In the end we have a closed interval of length
less than E on which f changes sign. The IVT
guarantees that there is a zero of f in this interval. The
endpoints of this interval, which are known, must be
within of this zero.
4. Bisection Algorithm
The idea for the Bisection Algorithm is to cut the interval [a,b] you are given in half
(bisect it) on each iteration by computing the midpoint xmid. The midpoint will
replace either a or b depending on if the sign of f(xmid) agrees with f(a) or f(b).
Step 1: Compute xmid = (a+b)/2
Step 2: If sign(f(xmid)) = 0 then end algorithm
else If sign(f(xmid)) = sign(f(a)) then a = xmid
else b = xmid
Step 3: Return to step 1
f(a)
f(b)
a b
root
xmid This shows how the points a, b
and xmid are related.
f(x)
5. Lets apply the Bisection Method to the same function as we did for the Regula-
Falsi Method. The equation is: x3
-2x-3=0, the function is: f(x)=x3
-2x-3.
This function has a root on the interval [0,2]
Iteration
a b xmid f(a) f(b) f(xmid)
1 0 2 1 -3 1 -4
2 1 2 1.5 -4 1 -2.262
3 1.5 2 1.75 -2.262 1 -1.140
4 1.75 2 1.875 -1.140 1 -.158
6. As we mentioned earlier we mentioned that we could compute exactly how many
iterations we would need for a given amount of error.
The error is usually measured by looking at the width of the current interval you
are considering (i.e. the distance between a and b). The width of the interval at
each iteration can be found by dividing the width of the starting interval by 2 for
each iteration. This is because each iteration cuts the interval in half. If we let the
error we want to achieve err and n be the iterations we get the following:
1log
2
21
2
2
1
1
1
−
−
=
−
=
−
=
−
=
+
+
+
err
ab
n
err
ab
aberr
ab
err
n
n
n
7. Example 1
Starting with the interval [1,2], find srqt(2) to within
two decimal places (to within an error of .01). The
function involved is f(x) = x2
-2. The following table
steps through the iteration until the size of the
interval, given in the last column, is less than .01.
The final result is the approximation 1.41406 for
the sqrt(2). This is guaranteed by the algorithm to
be within .01 (actually, to within 1/128) of sqrt(2).
In reality it agrees with sqrt(2) to three decimal
places, not just two.
9. Example 2
•Consider finding the root of f(x) = e-x
(3.2 sin(x)
- 0.5 cos(x)) on the interval [3, 4], this time
with εstep = 0.001, εabs = 0.001.
•Table 1. Bisection method applied to f(x) = e-
x
(3.2 sin(x) - 0.5 cos(x)).
10. a b f(a) f(b) c = (a + b)/2 f(c) Update new b − a
3.0 4.0 0.047127 -0.038372 3.5 -0.019757 b = c 0.5
3.0 3.5 0.047127 -0.019757 3.25 0.0058479 a = c 0.25
3.25 3.5 0.0058479 -0.019757 3.375 -0.0086808 b = c 0.125
3.25 3.375 0.0058479 -0.0086808 3.3125 -0.0018773 b = c 0.0625
3.25 3.3125 0.0058479 -0.0018773 3.2812 0.0018739 a = c 0.0313
3.2812 3.3125 0.0018739 -0.0018773 3.2968 -0.000024791 b = c 0.0156
3.2812 3.2968 0.0018739 -0.000024791 3.289 0.00091736 a = c 0.0078
3.289 3.2968 0.00091736 -0.000024791 3.2929 0.00044352 a = c 0.0039
3.2929 3.2968 0.00044352 -0.000024791 3.2948 0.00021466 a = c 0.002
3.2948 3.2968 0.00021466 -0.000024791 3.2958 0.000094077 a = c 0.001
3.2958 3.2968 0.000094077 -0.000024791 3.2963 0.000034799 a = c 0.0005