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tolerance of 0.001
+ For the function F(x) = 24 – 14.2 + 60.rº – 70x...
For the function F(x) = 24 – 14x² + 60.x2 – 702 find minimum value using...
For the function F(x) = 24 – 14x² + 60.x2 – 702 find minimum value using two methods - a. Newton's method starting with initial point of 1 b. Golden section in the interval [0,2] required tolerance =0.001
For the function F(x) = find minimum value using two methods - a. Newton's method starting...
For the function F(x) =
find minimum value using two methods -
a. Newton's method starting with initial point of 1
b. Golden section in the interval [0,2]
required tolerance =0.001
clearvars close all clc tol = 0.0001; % this is the tolerance for root identification xold...
clearvars
close all
clc
tol = 0.0001; % this is the tolerance for root identification
xold = 0.5; % this is the initial guess
test = 1; % this simply ensures we have a test value to enter the loop below.
%If we don't preallocate this, MATLAB will error when it trys to start the
%while loop below
k = 1; %this is the iteration counter. Similar to "test" we need to preallocate it
%to allow the while loop to...
3. Write a code to find 3 roots of the function f(x) 2r3-4x2 -22x +24 for the interval I-5, 5] co...
3. Write a code to find 3 roots of the function f(x) 2r3-4x2 -22x +24 for the interval I-5, 5] considering the following methods a) Bisection Method b) Newton's Method Hint: Plot a graph of f(x) and determine proper intervals and initial guesses for a) and b), respectively. 3. Write a code to find 3 roots of the function f(x) 2x3-4x2 -22x +24 for the interval [-5, 5] considering the following methods a) Bisection Method b) Newton's Method Hint: Plot...
3. Write a code to find 3 roots of the function f(x)-2x3-4x2-22x+24 for the interval -5, 5] consi...
3. Write a code to find 3 roots of the function f(x)-2x3-4x2-22x+24 for the interval -5, 5] considering the following methods a) Bisection Method b) Newton's Method Hint: Plot agraph of f(x) and determine proper intervals and initial guesses for a) and b), respectively
3. Write a code to find 3 roots of the function f(x)-2x3-4x2-22x+24 for the interval -5, 5] considering the following methods a) Bisection Method b) Newton's Method Hint: Plot agraph of f(x) and determine proper intervals...
1. Determine the root of function f(x)= x+2x-2r-1 by using Newton's method with x=0.8 and error,...
1. Determine the root of function f(x)= x+2x-2r-1 by using Newton's method with x=0.8 and error, e=0.005. 2. Use Newton's method to approximate the root for f(x) = -x-1. Do calculation in 4 decimal points. Letx=1 and error, E=0.005. 3. Given 7x)=x-2x2+x-3 Use Newton's method to estimate the root at 4 decimal points. Take initial value, Xo4. 4. Find the root of f(x)=x2-9x+1 accurate to 3 decimal points. Use Newton's method with initial value, X=2
2. Find a root ofthe functionf(x)=cos(x) +sin(x)-2x2 to fourdeci mal places for!f(xn +1 )1< 0.001...
2. Find a root ofthe functionf(x)=cos(x) +sin(x)-2x2 to fourdeci mal places for!f(xn +1 )1< 0.001 and Ixn-1-Xnl0.001 for each of the following rootfinding methods and initial guesses: a) Newton's Method, for xo = 0.2. b) Secant Method, for x-,-0.2 and xo = 0.5. c) Considering the following fixed point problern for xo=0.2 cos(xn)sin(n) d) Write a code to approximate the root of f(x) for each a), b) andc
2. Find a root ofthe functionf(x)=cos(x) +sin(x)-2x2 to fourdeci mal places for!f(xn...
Let F = (2,1,1) be a vector field in Rº a.) Show that F is a...
Let F = (2,1,1) be a vector field in Rº a.) Show that F is a conservative vector field. b.) Find the potential function of F. In other words, find a scalar function f(x, y, z) such that ✓ f = 7. Please show all steps. c.) Let C be any smooth curve starting at (1,1,1) and ending at (e, e, 1). Compute (Fdi. С
course: Numerical analysis 3. Consider Rosenbrock's banane valley function f(x,y) = (x-1) + 100 (4-x², henceforth...
course: Numerical analysis
3. Consider Rosenbrock's banane valley function f(x,y) = (x-1) + 100 (4-x², henceforth called the banana function. (a) Compute the gradient I f(x,y) of the banana function (6) Using (xo, Yo) = (-1.2, 1.0) as an initial point perform one iteration of the method of steepest, descent to explicitly find (X,Y). Refer to attached graph of level curves of the banana function. (XY)(-1.0301067/27..., 1.069344-19888...) and f(X,Y) S 401280972736-n, (c) Using (xoxo) = (-1-2, 1.0) as an initial...
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for X over [5 61, and ...
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for X over [5 61, and Y over [-4,-2]," b. Draw the contour plot for X over [0 10], and Y over [-4,-2] and values for the contours 1.25 1.5 2 25 3 of V c. Write an m-file to find the minimum of the function using the gradient descent method. Use a starting value of [4,-4].
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for...
For the function F(x) = 24 – 14x² + 60.x2 – 702 find minimum value using two methods - a. Newton's method starting with initial point of 1 b. Golden section in the interval [0,2] required tolerance =0.001
For the function F(x) =
find minimum value using two methods -
a. Newton's method starting with initial point of 1
b. Golden section in the interval [0,2]
required tolerance =0.001
clearvars
close all
clc
tol = 0.0001; % this is the tolerance for root identification
xold = 0.5; % this is the initial guess
test = 1; % this simply ensures we have a test value to enter the loop below.
%If we don't preallocate this, MATLAB will error when it trys to start the
%while loop below
k = 1; %this is the iteration counter. Similar to "test" we need to preallocate it
%to allow the while loop to...
3. Write a code to find 3 roots of the function f(x) 2r3-4x2 -22x +24 for the interval I-5, 5] considering the following methods a) Bisection Method b) Newton's Method Hint: Plot a graph of f(x) and determine proper intervals and initial guesses for a) and b), respectively. 3. Write a code to find 3 roots of the function f(x) 2x3-4x2 -22x +24 for the interval [-5, 5] considering the following methods a) Bisection Method b) Newton's Method Hint: Plot...
3. Write a code to find 3 roots of the function f(x)-2x3-4x2-22x+24 for the interval -5, 5] considering the following methods a) Bisection Method b) Newton's Method Hint: Plot agraph of f(x) and determine proper intervals and initial guesses for a) and b), respectively
3. Write a code to find 3 roots of the function f(x)-2x3-4x2-22x+24 for the interval -5, 5] considering the following methods a) Bisection Method b) Newton's Method Hint: Plot agraph of f(x) and determine proper intervals...
1. Determine the root of function f(x)= x+2x-2r-1 by using Newton's method with x=0.8 and error, e=0.005. 2. Use Newton's method to approximate the root for f(x) = -x-1. Do calculation in 4 decimal points. Letx=1 and error, E=0.005. 3. Given 7x)=x-2x2+x-3 Use Newton's method to estimate the root at 4 decimal points. Take initial value, Xo4. 4. Find the root of f(x)=x2-9x+1 accurate to 3 decimal points. Use Newton's method with initial value, X=2
2. Find a root ofthe functionf(x)=cos(x) +sin(x)-2x2 to fourdeci mal places for!f(xn +1 )1< 0.001 and Ixn-1-Xnl0.001 for each of the following rootfinding methods and initial guesses: a) Newton's Method, for xo = 0.2. b) Secant Method, for x-,-0.2 and xo = 0.5. c) Considering the following fixed point problern for xo=0.2 cos(xn)sin(n) d) Write a code to approximate the root of f(x) for each a), b) andc
2. Find a root ofthe functionf(x)=cos(x) +sin(x)-2x2 to fourdeci mal places for!f(xn...
Let F = (2,1,1) be a vector field in Rº a.) Show that F is a conservative vector field. b.) Find the potential function of F. In other words, find a scalar function f(x, y, z) such that ✓ f = 7. Please show all steps. c.) Let C be any smooth curve starting at (1,1,1) and ending at (e, e, 1). Compute (Fdi. С
course: Numerical analysis
3. Consider Rosenbrock's banane valley function f(x,y) = (x-1) + 100 (4-x², henceforth called the banana function. (a) Compute the gradient I f(x,y) of the banana function (6) Using (xo, Yo) = (-1.2, 1.0) as an initial point perform one iteration of the method of steepest, descent to explicitly find (X,Y). Refer to attached graph of level curves of the banana function. (XY)(-1.0301067/27..., 1.069344-19888...) and f(X,Y) S 401280972736-n, (c) Using (xoxo) = (-1-2, 1.0) as an initial...
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for X over [5 61, and Y over [-4,-2]," b. Draw the contour plot for X over [0 10], and Y over [-4,-2] and values for the contours 1.25 1.5 2 25 3 of V c. Write an m-file to find the minimum of the function using the gradient descent method. Use a starting value of [4,-4].
1). For the function, f(x) X-4X+2XY+2Y2+2Y+14 a. Plot the surface function for...
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