Numerical Methods for Engineers
Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 11, Problem 16P

Use the software package of your choice to obtain a solution, calculate the inverse, and determine the condition number (without scaling) based on the row-sum norm for

(a) [ 1 4 9 4 9 16 9 16 25 ] { x 1 x 2 x 3 } = { 14 29 50 }

(b) [ 1 4 9 16 4 9 16 25 9 16 25 36 16 25 36 49 ] { x 1 x 2 x 3 x 4 } = { 30 54 86 126 }

In both cases, the answers for all the x's should be 1.

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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

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Interpolation | Lecture 43 | Numerical Methods for Engineers; Author: Jffrey Chasnov;https://www.youtube.com/watch?v=RpxoN9-i7Jc;License: Standard YouTube License, CC-BY