solve the program using fortan and dont plagarise or copy from other sources thank you 1. (a) Consider the polynomial (x − 1)(x − 2) = x² -3x+2 which has exact roots x = 1 andx = 2. Suppose some numerical algorithm finds approximate roots equal to ✰ = 1.1 and= 1.9. For each root determine the forward error and the relative forward error. Then,for each approximate root, find a perturbed quadratic, that is as close to the originalquadratic as possible, such that the approximate root to the original quadratic is theexact root to the perturbed quadratic. For each approximate root, what is the backwarderror and what is the relative backward error?(b) For each approximate root, draw a diagram like the ones we've seen in the coursenotes, showing the relationship between the original problem the perturbed problem, theexact root, and the approximate root. Make sure to include the value of the forward errorand the backward error in the diagram.

Step 1: Step 2: Step 3: Step 4:

Answered: 1. (a) Consider the polynomial (x −…

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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1) Find the 3rd order polynomial that satisfies the data of water for saturation temperature and pressure. By using the predicted polynomial compute the saturation pressure at 65 C. Temp(C) 0 Pre. (kPa) .6108 1.227 2.337 4.241 7.375 12.335 19.92 31.16 47.36 70.11 101.33 10 20 30 40 50 60 70 80 90 100 2) A vapor pressure vs. temperature thermodynamic process has the following data.Write a MATLAB program to calculate the values of constants A and B in following equation. B og( P°) = A- T+ 273.15 Temp (C) | -36.7 | -19.6 -11.5 Pre. (kPa) -2.6 7.6 15.4 26.1 42.2 60.6 80.1 1 5 10 20 40 60 100 200 400 760 3) The experimental velocity of an incompressible fluid in a pipe of radius 1 m is tabulated as below: Second Class \ Lec. 5 47 Computer Programming (II) Dr. Saad Raheem r (m) 0.0 0,1 0,2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 V 1.0 0.99 0.96 0.91| 0.84 0.75 0.64 0.51 0.36 0.19 0.0 Where: r is the distance from the centre of the pipe and u is the velocity of the fluid. Write a MATLAB program to…
4. The following algorithm for approximating roots combines the bisection method with Newton's method and ensures the convergence even in the case where Newton's method fail to converge. Choose an interval [a, b] such that f(a)f(b) ≤ 0. Compute initial approximation xo = (a+b)/2 of the root using the bisection method. For i=1,2,... Compute x₁ using Newton's method and X₁-1. If x₁ [a, b], set x₁ = (a + b)/2 (from bisection). Check for convergence. If f(a) f(xi) ≤0 set b = xi, else set a = xį. (a) Implement this algorithm in a PYTHON function with the following specifications: def findzero (a, b, tol, maxit, f, df) # Input: # a, b = The endpoints of the interval # tol = The required tolerance # maxit = Maximum number of iterations # f, df = The function and its derivative # Output: # star #niter # ierr # # # approximation of root = number of iterations for convergence 0, the method converged 1, df was zero or undefined 2, maximum number of iterations has been reached return xstar, niter,…
f(x) = x3 – 3x – 4 Consider the function on the interval [2,2.5].When the tolerence value is 10-5 and maximum number of iterations is 100, find the number of iterations that MATLAB made to get last approximation of the root by using MATLAB function file of Bisection method. Your answer: O 14 O 15 17 O 16

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