Third Order Convergence for Reciprocal

09202021, 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)=1xx^2x^3.... Then this term is collapsed to (1x)(1x^2)(1x^4)(1x^8)... until x^(2k) is small. There's a similar formula for 1/(1x).
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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Third Order Convergence for Reciprocal  Albert Chan  09192021, 04:14 PM
RE: Third Order Convergence for Reciprocal  Albert Chan  09192021, 04:47 PM
RE: Third Order Convergence for Reciprocal  Albert Chan  09192021, 05:59 PM
RE: Third Order Convergence for Reciprocal  lyuka  09202021, 04:33 AM
RE: Third Order Convergence for Reciprocal  Albert Chan  09202021, 01:20 PM
RE: Third Order Convergence for Reciprocal  ttw  09202021 10:14 AM
RE: Third Order Convergence for Reciprocal  Albert Chan  09222021, 10:32 AM
RE: Third Order Convergence for Reciprocal  Namir  09252021, 09:39 PM

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