By Clark Howard
Clark Howard, the bestselling writer of Get Clark shrewdpermanent and host of the nationally syndicated radio application The Clark Howard convey, desires to enable you to get the easiest bang on your buck--whether you're on the grocery store, purchasing new outfits, renovating your place, or going to the films. how to pay $12.95 for a CD that charges $19.95. discover why a $90 VCR simply may go larger than a $300 VCR.
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Extra resources for Clark's Big Book of Bargains
In general, the attitude expressed here is that any model is at best an approximation of reality, and a good approximation of the model's solutions may be as useful an answer as the exact solution. The advantage of numerical methods is that page_47 Page 48 we can analyze more realistic models, reducing the approximation errors arising from using an excessively simple model. The cost of using numerical methods is the inevitable numerical error, but the gain from model realism is often well worth the cost.
Anyone using a machine with 12 significant digits cannot be confident about any digit in a solution of Hnx = b if n exceeds 9. This is not a rare example. While in some sense "most" matrices have low to moderate condition numbers, many intuitive procedures, such as least squares approximation procedures, lead to poorly conditioned problems with disastrously high condition numbers. The error bounds we computed were approximate upper bounds, but that was under the assumption that we could exactly solve the perturbed system.
In fact, generally, perturbation methods are not discussed in numerical analysis texts. We include both approaches in this book because both are useful in economics, and there is growing interest in merging numerical and symbolic methods to create hybrid methods. We will see an example of the possible synergies between numerical and symbolic methods in chapter 15. 10 Evaluating the Error in the Final Result When we have completed a computation using either numerical or symbolic methods, we want to know how good our answer is.