This is taken from Trefethen and Bau, 13.3. Why is there a difference in accuracy between evaluating near 2 the expression $(x-2)^9$ and this expression: $$x^9 – 18x^8 + 144x^7 -672x^6 + 2016x^5 – 4032x^4 + 5376x^3 – 4608x^2 + 2304x – 512 $$ Where exactly is the problem? Thanks.

I have the number 0.101 in binary. I want to round it to 2 places after the radix point using the algorithm rounding to the nearest. Here is how I do it. If I want to have two places, then I will have one of the two possible resulting numbers: 0.10 or 0.11. Let’s see […]

The crucial requirement for using root isolation methods based on Vincent’s theorem is that the input polynomial does not have multiple zeros. One way to remove the multiple zeros is to use polynomial GCD. However, when it is implemented with the usual floating-point numbers (IEEE doubles), most probably the various rounding errors will cause the […]

I’m having trouble completing a question that deals with the IEEE 754 32-bit floating point format, primarily because I don’t know how to use it. I was hoping someone here could clarify for me using the following example (or link to relevant sources that may reveal how I can complete the problem). Convert 4.625 to […]

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