Question 5 Numerical Approximation Methods basic ideas: Please write the basic idea (with key equations), application example, advantages and limitations of the following numerical approximation methods for solving linear/nonlinear equations. Please also state cases/examples for which one method can provide good result, but other may not. 1) Relaxation method 2) Binary search method 3) Newton's method 4) Secant method

Question 5 Numerical Approximation Methods basic ideas: Please write the basic idea (with key equations), application example, advantages and limitations of the following numerical approximation methods for solving linear/nonlinear equations. Please also state cases/examples for which one method can provide good result, but other may not. 1) Relaxation method 2) Binary search method 3) Newton's method 4) Secant method

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter4: Selection Structures

Section: Chapter Questions

Problem 14PP

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Question 5 When writing a recursive method, O you do not need to know ahead of time exactly how many levels of recursion will occur. O you must keep count of how many recursion call levels you have traversed. O you must make sure the method does not take any input parameters.
TROUBLESHOOTING: Fix the errors in the code below and run the script with your modified code function [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % Solves Ax = b by Gauss-Seidel method with relaxation. % USAGE: [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % INPUT: % func = handle of function that returns improved x using % x = starting solution vector % maxIter = allowable number of iterations (default is 500) % epsilon = error tolerance (default is 1.0e-9) % OUTPUT: % x = solution vector % numIter = number of iterations carried out % omega = computed relaxation factor if nargin < 4; epsilon = 1.0e-9; end if nargin < 3; maxIter = 500; end k = 10; p = 1; omega = 1; for numIter = 1:maxIter xOld = x; x = feval(func,x,omega); dx = sqrt(dot(x - xOld,x - xOld)); if dx < epsilon; return; end if numIter == k; dx1 = dx; end if numIter == k + p omega = 2/(1 + sqrt(1 - (dx/dx1)ˆ(1/p))); end end error(’Too many iterations’)
ASAP Solution needed / Solution You're given a string of words. You need to find the word "Nemo", and return a string like this: "I found Nemo at [the order of the word you find Nemo]!" If you can't find Nemo, return "I can't find Nemo :(". Examples findNemo ("I am finding Nemo !") → "I found Nemo at 4!" wwwwwwww ➡ "I found Nemo at 1!" findNemo ("Nemo is me") www findNemo ("I Nemo am") wwwwwwwww "I found Nemo at 2!" (Ctrl)
Python question Analysis: Computational Complexity (Q14-15) In this section, you are asked to analyse the worst-case computational time complexity of Python functions. Always identify the order of growth in the tightest and simplest possible form using big-O notation, e.g., write O(n) instead of O(2n+n/2). Question 14 (Complexity 1) State the overall worst-case time complexity of the below function and provide a short explanation of your answer. The function accepts an integer n as input. def mystery(n): num = 1 count = 0 while num < n: num = num*2 count += 1 return count Question 15 (Complexity 2) State the overall worst-case time complexity of the below function and provide a short explanation of your answer. The function is supposed to return a list, res, containing the duplicated elements in the given list , lst, of size n. Analyse the function in terms of the length of the list, n. def duplicate_values(lst): res = [] for i in range(len(lst)):…
ASAP Solution needed / Solution You're given a string of words. You need to find the word "Nemo", and return a string like this: "I found Nemo at [the order of the word you find Nemo]!" If you can't find Nemo, return "I can't find Nemo :(". Examples findNemo ("I am finding Nemo !") → "I found Nemo at 4!" wwwwwwwww findNemo ("Nemo is me") ➡ "I found Nemo at 1!" findNemo ("I Nemo am") ➡ "I found Nemo at 2!" wwwwwwww (Ctrl)
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Mailings Review View Help AaBbC AaBbCcD AaBbCcD AaBbCc Aa Heading 1 T Normal 1No Spac. Heading 2 Hea Paragraph Styles 8. Consider the following equation for the sum of a finite arithmetic series: S, = n(a, ta where n is the number of elements in the series, a is the first element of the series, and a, is the last element of the series. Write a method that returns the sum of the elements stored in the array in 8 above. The array must be passed to the method as an argument. Your solution should implement the equation for the sum S.
If you try to solve a problem recursively, you should apply) find a recursive call that will lead towards one of the stopping cases find all the stopping cases and the values if needed at that case (select all that
JAVA Question 2: For two integers m and n, their GCD (Greatest Common Divisor) can be computed by a recursive method. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Method body: If m is 0, the method returns n. If n is 0, the method returns m. If neither is 0, the method can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n (or m % n). The recursive method cannot have loops. Note: although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. main method: Prompt and read in two numbers to find the greatest common divisor. Call the gcd method with the two numbers as its argument. Print the result to the monitor. Example program run: Enter m: 12 Enter n: 28 GCD(12,28) = 4 And here is what I have so far, package CSCI1302;import java.util.*;public class RecursionDemo { public static void…
Python only* Use recursive function*. Define colorListCircles with 2 parameters Use def to define colorListCircles with 2 parameters The colorListCircles function must draw concentric circles using colors from a list. It has two parameters: the first specifies the radius of the largest circle, and the second is a list of colors. The number of concentric circles drawn is the length of the list, and these circles are colored, from largest to smallest, by the colors in the list from first to last. When viewed as nested rings, all rings should have the same thickness. If the list is empty, nothing should be drawn. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order, you may not use any loops and you must use recursion. Also, you will still need to use drawDot. For full credit, your function should call drawDot in only one place, and should only contain one recursive call. Do not use any kind of loop Within the definition…
How to apply this python code in the problem? What are the base cases and recursive cases that should be used? def createList(n): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all the TODO for this function return [] def removeMultiples(x, arr): #Base Case/s #TODO: Add conditions here for your base case/s #if <condition> : #return <value> #Recursive Case/s #TODO: Add conditions here for your recursive case/s #else: #return <operation and recursive call> #remove the line after this once you've completed all the TODO for this function return [] def Sieve_of_Eratosthenes(list): #Base Case/s if len(list) < 1 : return list #Recursive Case/s else:…
Python only* Use recursive function*. Define colorListCircles with 2 parameters Use def to define colorListCircles with 2 parameters The colorListCircles function must draw concentric circles using colors from a list. It has two parameters: the first specifies the radius of the largest circle, and the second is a list of colors. The number of concentric circles drawn is the length of the list, and these circles are colored, from largest to smallest, by the colors in the list from first to last. When viewed as nested rings, all rings should have the same thickness. If the list is empty, nothing should be drawn. We will test both how many circles are drawn as well as whether the correct circles are drawn in the correct order, you may not use any loops and you must use recursion. Also, you will still need to use drawDot. For full credit, your function should call drawDot in only one place, and should only contain one recursive call. Do not use any kind of loop Within the definition…