Homework Answers
The substitution method we used for linear systems is the same method we will use for nonlinear systems. We solve one equation for one variable and then substitute the result into the second equation to solve for another variable, and so on. There is, however, a variation in the possible outcomes.
So, an initiative estimate of the root is needed.
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Which of the following is a requirement to use the Fixed- Point/Direct Substitution Method to find...
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The ...
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The derivative of the function can be approximately evaluated using finite-difference method. Consider the Forward and Centered finite-difference formulas Forward Finite-Difference Centered Finite-Difference 2h It is worthwhile to mention that modified secant method was derived based on the forward finite- difference formula. Develop a MATLAB functions that has the following syntax function [root,fx,ea,iter]-modnetraph (func,x0,h,es,maxit,sethod, varargin) % modnevtraph: root location zeroes of nonlinear equation f (x)...
true 1. Newton's method will always find a root of a smooth, differentiable, function with a...
true 1. Newton's method will always find a root of a smooth, differentiable, function with a root. a) b) false c) only with a good initial guess 2. Give one mathematical equation that defines an eigenvalue. Use A for the matrix and e for the eigenvalue and v for the eigenvector. 3: A program to do optimization can work on any number of independent variables. a) true b) false 4: Computing a FFT (Fast Fourier Transform) of a persons voice,...
(a) Given the following function f(x) below. Sketch the graph of the following function A1. f () 3 1, 12 5 marks (b) Ve...
(a) Given the following function f(x) below. Sketch the graph of the following function A1. f () 3 1, 12 5 marks (b) Verify from the graph that the interval endpoints at zo and zi have opposite signs. Use the bisection method to estimate the root (to 4 decimal places) of the equation 5 marks] (c) Use the secant method to estimate the root (to 4 decimal places) of the equation 6 marks that lies between the endpoints given. (Perform...
B. Implement the Newton-Raphson (NR) method for solving nonlinear equations in one dimension. The...
B. Implement the Newton-Raphson (NR) method for solving nonlinear equations in one dimension. The program should be started from a script M-file. Prompt the user to enter an initial guess for the root. -Use an error tolerance of 107, -Allow at most 1000 iterations. .The code should be fully commented and clear 2. a) Use your NR code to find the positive root of the equation given below using the following points as initial guesses: xo = 4, 0 and-1...
A. Implement the False-Position (FP) method for solving nonlinear equations in one dimension. The...
A. Implement the False-Position (FP) method for solving nonlinear equations in one dimension. The program should be started from a script M-file. -Prompt the user to enter lower and upper guesses for the root. .Use an error tolerance of 107. Allow at most 1000 iterations The code should be fully commented and clear " 1. Use your FP and NR codes and appropriate initial guesses to find the root of the following equation between 0 and 5. Plot the root...
Numerical method no programm needed 4. Use first three fixed point iterations to find the approximated...
Numerical method no programm needed
4. Use first three fixed point iterations to find the approximated so- lution of the following equation 2-e" +22 3 starting from Io = 1 and round the result to 4 significant digit. (Answer: r* 33 = 0.2459 ) =
II. Using Newton’s method, write a MATLAB program to find the fixed point of the following...
II. Using Newton’s method, write a MATLAB program to find the fixed point of the following function: ?(?) = √? + ?? accurate to at least 8 decimal places. (HINT: finding the fixed point of f(x) is the same as finding the zero of g(x) = f(x) − x. ) The output of this program should display in a single table (i) the solution for the fixed point, (ii) the initial guess, (iii) the number of iterations it took to...
Find an equation of the plane tangent to the following surface at the given point. yz...
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
Matlab only What is the function value at the estimated root after one iteration of the...
Matlab only
What is the function value at the estimated root after one iteration of the bisection method for the root finding equation: f(x) = x^3 -x -11 with xl = -4 and xu = 2.5? Select one: a.-0.7500 x O b.-3.2500 o co d. -10.6719 Which of the following statements is false? All open methods for root finding: Select one: a. Is sensitive to the shape of the function X b. Require two initial guesses to begin the algorithm...
Suppose you want to find a fixed point of a smooth function g(x) on the interval...
Suppose you want to find a fixed point of a smooth function g(x)
on the interval [a,b]
a. Give conditions which would be sufficient to show that fixed
point iteration on g(x), starting with some
[a,b], will converge to the fixed point p.
b. When is this convergence only linear?
c. When is this convergence only quadratic?
d. Suppose a smooth function f(x) has a root p with f '(p) != 0.
Assuming you choose the initial guess close enough...
. (25 points) The recurrence relation for the Newton's Raphson method is a)0.1.2 f(r.) F(z.) The derivative of the function can be approximately evaluated using finite-difference method. Consider the Forward and Centered finite-difference formulas Forward Finite-Difference Centered Finite-Difference 2h It is worthwhile to mention that modified secant method was derived based on the forward finite- difference formula. Develop a MATLAB functions that has the following syntax function [root,fx,ea,iter]-modnetraph (func,x0,h,es,maxit,sethod, varargin) % modnevtraph: root location zeroes of nonlinear equation f (x)...
true 1. Newton's method will always find a root of a smooth, differentiable, function with a root. a) b) false c) only with a good initial guess 2. Give one mathematical equation that defines an eigenvalue. Use A for the matrix and e for the eigenvalue and v for the eigenvector. 3: A program to do optimization can work on any number of independent variables. a) true b) false 4: Computing a FFT (Fast Fourier Transform) of a persons voice,...
(a) Given the following function f(x) below. Sketch the graph of the following function A1. f () 3 1, 12 5 marks (b) Verify from the graph that the interval endpoints at zo and zi have opposite signs. Use the bisection method to estimate the root (to 4 decimal places) of the equation 5 marks] (c) Use the secant method to estimate the root (to 4 decimal places) of the equation 6 marks that lies between the endpoints given. (Perform...
B. Implement the Newton-Raphson (NR) method for solving nonlinear equations in one dimension. The program should be started from a script M-file. Prompt the user to enter an initial guess for the root. -Use an error tolerance of 107, -Allow at most 1000 iterations. .The code should be fully commented and clear 2. a) Use your NR code to find the positive root of the equation given below using the following points as initial guesses: xo = 4, 0 and-1...
A. Implement the False-Position (FP) method for solving nonlinear equations in one dimension. The program should be started from a script M-file. -Prompt the user to enter lower and upper guesses for the root. .Use an error tolerance of 107. Allow at most 1000 iterations The code should be fully commented and clear " 1. Use your FP and NR codes and appropriate initial guesses to find the root of the following equation between 0 and 5. Plot the root...
Numerical method no programm needed
4. Use first three fixed point iterations to find the approximated so- lution of the following equation 2-e" +22 3 starting from Io = 1 and round the result to 4 significant digit. (Answer: r* 33 = 0.2459 ) =
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
Matlab only
What is the function value at the estimated root after one iteration of the bisection method for the root finding equation: f(x) = x^3 -x -11 with xl = -4 and xu = 2.5? Select one: a.-0.7500 x O b.-3.2500 o co d. -10.6719 Which of the following statements is false? All open methods for root finding: Select one: a. Is sensitive to the shape of the function X b. Require two initial guesses to begin the algorithm...
Suppose you want to find a fixed point of a smooth function g(x)
on the interval [a,b]
a. Give conditions which would be sufficient to show that fixed
point iteration on g(x), starting with some
[a,b], will converge to the fixed point p.
b. When is this convergence only linear?
c. When is this convergence only quadratic?
d. Suppose a smooth function f(x) has a root p with f '(p) != 0.
Assuming you choose the initial guess close enough...
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