(2) (a) Refer to the course notes on Algorithm Stability and note the definition for En· Using an integration by parts approach we were able to show that, En = 1 nEn-1. Once we were able to figure out a value for E₁, the above recurrence formula suggested a straightforward way to obtain whatever En values we wanted, for n > 1. However, the numerical results showed that something went terribly wrong with the computation. Explain in your own words why the computation goes terribly wrong. (b) In the course notes, we saw that a simple rewriting of the recurrence formula, and a fairly rough approximation for En, for a larger value of n, leads to an algorithm which provides very accurate results for smaller values of n. Explain in your own words why this approach work so well. (c) Implement the two algorithms in Fortran to reproduce the numerical results shown in the notes. Verify that you get the same results. (Start by editing the Stirling Approx- imation program for n! from Assignment #1.)

(2) (a) Refer to the course notes on Algorithm Stability and note the definition for En· Using an integration by parts approach we were able to show that, En = 1 nEn-1. Once we were able to figure out a value for E₁, the above recurrence formula suggested a straightforward way to obtain whatever En values we wanted, for n > 1. However, the numerical results showed that something went terribly wrong with the computation. Explain in your own words why the computation goes terribly wrong. (b) In the course notes, we saw that a simple rewriting of the recurrence formula, and a fairly rough approximation for En, for a larger value of n, leads to an algorithm which provides very accurate results for smaller values of n. Explain in your own words why this approach work so well. (c) Implement the two algorithms in Fortran to reproduce the numerical results shown in the notes. Verify that you get the same results. (Start by editing the Stirling Approx- imation program for n! from Assignment #1.)

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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