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Square Root via Newton’s Method 0 | Index << >> |
Apply Newton iteration ⍺
times to find the square root of ⍵ .
sqrt0←{
W←⍵
f←{2÷⍨W+⍺÷⍵}
⍺ {1≥⍺:⍵ ⋄ (⍺-1)∇ ⍵,f ¯1↑⍵} 1 ⍝ f⍣(⍳⍺)⊢1
}
⊢ t← 8 sqrt0 2
1 1.5 1.41667 1.41422 1.41421 1.41421 1.41421 1.41421
(15⍕ ⍪t), ' ', ¯6⍕ ⍪ 2-t×t
1.000000000000000 1.00000E0
1.500000000000000 ¯2.50000E¯1
1.416666666666667 ¯6.94444E¯3
1.414215686274510 ¯6.00730E¯6
1.414213562374690 ¯4.51061E¯12
1.414213562373095 4.44089E¯16
1.414213562373095 4.44089E¯16
1.414213562373095 4.44089E¯16
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