A tight bound for approximating the square root

Nader H. Bshouty, Yishay Mansour, Baruch Schieber, Prasoon Tiwari

Research output: Contribution to journalArticlepeer-review


We prove an Ω(log log(1/ε)) lower bound on the depth of any computation tree and any RAM program with operations {+, -, *, /, ⌊·⌋, not, and, or, xor}, unlimited power of answering YES/NO questions, and constants {0,1} that computes √x to accuracy ε, for all x ∈ [1,2]. Since the Newton method achieves such an accuracy in O(log log(1/ε)) depth, our bound is tight.

Original languageEnglish
Pages (from-to)211-213
Number of pages3
JournalInformation Processing Letters
Issue number4
StatePublished - 28 Aug 1997


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