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Third Order Convergence for Reciprocal
09-20-2021, 10:14 AM
Post: #5
RE: Third Order Convergence for Reciprocal
There is an old method for matrix inverse that can be used with ordinary numbers. The idea is that 1/(1+x)=1-x-x^2-x^3.... Then this term is collapsed to (1-x)(1-x^2)(1-x^4)(1-x^8)... until x^(2k) is small. There's a similar formula for 1/(1-x).

The point is that one computes x^2 (1 multiplication) and gets increasingly accurate approximations with each multiplication. I think it's of exponential order but I don't remember.

Let's count: 3 multiplications for order 4, 5 multiplications for order 8, 7 multiplications for order 16, 9 multiplications for order 32...
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RE: Third Order Convergence for Reciprocal - ttw - 09-20-2021 10:14 AM

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