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