MATH6800/CSCI6800 Computational Linear Algebra

Homework 1.

Due: Monday, September 11, 2000.

1.

Demmel, Question 1.1.

2.

Demmel, Question 1.3.

3.

Demmel, Question 1.5.

4.

Demmel, Question 1.9. Note that for x close to zero, we have the power series representation

$$\begin{eqnarray*} \ln (1+x) &=& \sum_{i=1}^{\infty} (-1)^{i-1} \frac{x^i}{i} \\ &=& x - \frac{x^2}{2} + \frac{x^3}{3} - \ldots \end{eqnarray*}$$

You need to use the fact that a number is stored as the closest floating point number, and an arithmetic operation preserves this property -- see the last paragraph on page 11 of the text.

5.

Demmel, Question 1.13. For the forward direction, try to provide a constructive proof, that is, define A using the inner product.

6.

Demmel, Question 1.20, part 1. This question requires the use of polyplot.m. Be careful about the use of i when defining complex conjugate roots, since polyplot.m redefines this quantity.

	John Mitchell
	Amos Eaton 325
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	mitchj@rpi.edu
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