Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 0.1, Problem 6E

Explain how to evaluate the polynomial for a given input x , using as few operations as possible. How many multiplications and how many additions are required?

a. P x = a 0 + a 5 x 5 + a 10 x 10 + a 15 x 15
b. P x = a 7 x 7 + a 12 x 12 + a 17 x 17 + a 22 x 22 + a 27 x 27

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Chapter 0 Solutions

Numerical Analysis

Ch. 0.1 - Rewrite the following polynomials in nested form...Ch. 0.1 - Rewrite the following polynomials in nested form...Ch. 0.1 - Evaluate P(x)=x64x4+2x2+1 at x=1/2 by considering...Ch. 0.1 - Evaluate the nested polynomial with base points...Ch. 0.1 - Evaluate the nested polynomial with base points...Ch. 0.1 - Explain how to evaluate the polynomial for a given...Ch. 0.1 - How many additions and multiplications are...Ch. 0.1 - Use the function nest to evaluate P(x)=1+x+...+x50...Ch. 0.1 - Use nest.m to evaluate P(x)=1x+x2x3+...+x98x99 at...Ch. 0.2 - Find the binary representation of the base 10...
Ch. 0.2 - Find the binary representation of the base 10...Ch. 0.2 - Convert the following base 10 numbers to binary....Ch. 0.2 - Convert the following base 10 numbers to binary....Ch. 0.2 - Find the first bits in the binary representation...Ch. 0.2 - Find the first 15 bits in the binary...Ch. 0.2 - Convert the following binary numbers to base :...Ch. 0.2 - Convert the following binary numbers to base...Ch. 0.3 - Convert the following base 10 numbers to binary...Ch. 0.3 - Convert the following base 10 numbers to binary...Ch. 0.3 - For which positive integers k can the number 5+2k...Ch. 0.3 - Find the largest integer k for which in double...Ch. 0.3 - Do the following sums by hand in IEEE double...Ch. 0.3 - Do the following sums by hand in IEEE double...Ch. 0.3 - Prob. 7ECh. 0.3 - Is 1/3+2/3 exactly equal to I in double precision...Ch. 0.3 - Prob. 9ECh. 0.3 - Prob. 10ECh. 0.3 - Does the associative law hold for IEEE computer...Ch. 0.3 - Prob. 12ECh. 0.3 - Prob. 13ECh. 0.3 - Prob. 14ECh. 0.3 - Do the following operations by hand in IEEE double...Ch. 0.3 - Prob. 16ECh. 0.4 - Identify for which values of x there is...Ch. 0.4 - Find the roots of the equation x2+3x814=0 with...Ch. 0.4 - Explain how to most accurately compute the two...Ch. 0.4 - Evaluate the quantity xx2+17x2 where x=910 ,...Ch. 0.4 - Evaluate the quantity 16x4x24x2 where x=812 ,...Ch. 0.4 - Prove formula (0.14).Ch. 0.4 - Calculate the expressions that follow in double...Ch. 0.4 - Prob. 2CPCh. 0.4 - Prob. 3CPCh. 0.4 - Prob. 4CPCh. 0.4 - Prob. 5CPCh. 0.5 - Prob. 1ECh. 0.5 - Find c satisfying the Mean Value Theorem for f(x)...Ch. 0.5 - Find c satisfying the Mean Value Theorem for...Ch. 0.5 - Find the Taylor polynomial of degree 2 about the...Ch. 0.5 - Find the Taylor polynomial of degree 5 about the...Ch. 0.5 - a. Find the Taylor polynomial of degree 4 for ...Ch. 0.5 - Carry out Exercise 6 (a)-(d) for f(x)=lnx .Ch. 0.5 - (a) Find the degree 5 Taylor polynomial centered...Ch. 0.5 - Prob. 9E
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