4 Problem Solving14. (5 points each, Total 10 points) Solve the following recurrences. Give tight, i.e. O(:), bounds. Ifyou are using Master Method, provide the case of the Master Method that you applied.а. Т(п) %3D 49T (")+n* lgn=b. Т(п) — 4T (") + ntog34

Answered: Image /qna-images/answer/1b4d6b4f-ec28-4c27-b1b4-3d562e2c59c5.jpg

Answered: you are using Master Method, provide…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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A2 Algorithm - Newton’s Method Input x0, xTol iters = 1 dx = -f(x0)/fDeriv(x0) (* fcns f and fDeriv *) root = x0 + dx While (Abs(dx) > xTol) dx = -f(root)/fDeriv(root) root = root + dx iters = iters + 1 End of while Return root, iters Exercise 2. Use the Newton Raphson method to estimate the root of f (x) = e − x −1, employing an initial guess of x = 0. The tolerance is = 10−8 .
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SUCCESSIVE-OVER-RELAXATION Method 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’)
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4. Practice with the iteration method. We have already had a recurrence relation ofan algorithm, which is T(n) = 4T(n/2) + n log n. We know T(1) ≤ c.(a) Solve this recurrence relation, i.e., express it as T(n) = O(f(n)), by using the iteration method.Answer:(b) Prove, by using mathematical induction, that the iteration rule you have observed in 4(a) is correct and you have solved the recurrence relation correctly. [Hint: You can write out the general form of T(n) at the iteration step t, and prove that this form is correct for any iteration step t by using mathematical induction.Then by finding out the eventual number of t and substituting it into your generalform of T(n), you get the O(·) notation of T(n).]

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you are using Master Method, provide the case of the Master Method that you applied. a. T(n) = 49T () + n* lgn b. T(n) = 4T (4) + n!o934