Numerical Methods For Engineers, 7 Ed
Numerical Methods For Engineers, 7 Ed
7th Edition
ISBN: 9789352602131
Author: Canale Chapra
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 10, Problem 15P

Determine the condition number for the following system using the row-sum norm. Do not normalize the system.

[ 1 4 9 16 4 9 16 25 9 16 25 36 16 25 25 36 36 49 49 64 25 36 49 64 81 ]

How many digits of precision will be lost due to ill-conditioning?

(b) Repeat (a), but scale the matrix by making the maximum element in each row equal to one.

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18. If m n compute the gcd (a² + 1, a² + 1) in terms of a. [Hint: Let A„ = a² + 1 and show that A„|(Am - 2) if m > n.]
For each real-valued nonprincipal character x mod k, let A(n) = x(d) and F(x) = Σ : dn * Prove that F(x) = L(1,x) log x + O(1). n
By considering appropriate series expansions, e². e²²/2. e²³/3. .... = = 1 + x + x² + · ... when |x| < 1. By expanding each individual exponential term on the left-hand side the coefficient of x- 19 has the form and multiplying out, 1/19!1/19+r/s, where 19 does not divide s. Deduce that 18! 1 (mod 19).

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Numerical Methods For Engineers, 7 Ed

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