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Calculating Catastrophe : Gordon Woo :
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Please try again later. Format: Paperback Verified Purchase. Very knowledgeable treatment of a wide variety of catastrophe issues and measurements. But the exposition could be clearer and the mathematics introduced more intuitively. It is a very useful book but takes some work to plow through. One person found this helpful. See the review. Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more about Amazon Giveaway. This item: Calculating catastrophe. Set up a giveaway. There's a problem loading this menu right now.
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Notice that the solution of greater magnitude is accurate to ten digits, but the first nonzero digit of the solution of lesser magnitude is wrong. Because of the subtraction that occurs in the quadratic equation, it does not constitute a stable algorithm to calculate the two roots. A careful floating-point computer implementation combines several strategies to produce a robust result. To illustrate the instability of the standard quadratic formula compared this formula, consider a quadratic equation with roots 1. To 16 significant digits, roughly corresponding to double-precision accuracy on a computer, the monic quadratic equation with these roots may be written as.
Using the standard quadratic formula and maintaining 16 significant digits at each step, the standard quadratic formula yields.
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To illustrate this, consider the following quadratic equation, adapted from Kahan : . This is despite the fact that superficially, the problem seems to require only 11 significant digits of accuracy for its solution. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. This article may be confusing or unclear to readers.
In particular, there are various uses of accuracy and precision they are not the same and significance, with unclear relation. Please make the meaning explicit, with a specific example relating all three, and how to obtain them from digits of a number does the digit before the decimal point count or not, etc. Please help us clarify the article.
There might be a discussion about this on the talk page. July Learn how and when to remove this template message. Categories : Numerical analysis.