Iterative Methods For Reciprocal Square Roots
The following are iterative methods for finding the reciprocal square root of S which is . Once it has been found, find by simple multiplication: . These iterations involve only multiplication, and not division. They are therefore faster than the Babylonian method. However, they are not stable. If the initial value is not close to the reciprocal square root, the iterations will diverge away from it rather than converge to it. It can therefore be advantageous to perform an iteration of the Babylonian method on a rough estimate before starting to apply these methods.
- One method is found by applying Newton's method to the equation . It converges quadratically:
- Another iteration obtained by Halley's method, which is the Householder's method of order two, converges cubically, but involves more operations per iteration:
Read more about this topic: Methods Of Computing Square Roots
Famous quotes containing the words methods, reciprocal, square and/or roots:
“The philosopher is in advance of his age even in the outward form of his life. He is not fed, sheltered, clothed, warmed, like his contemporaries. How can a man be a philosopher and not maintain his vital heat by better methods than other men?”
—Henry David Thoreau (1817–1862)
“I had no place in any coterie, or in any reciprocal self-advertising. I stood alone. I stood outside. I wanted only to learn. I wanted only to write better.”
—Ellen Glasgow (1873–1945)
“I walked by the Union Square Bar, I was gonna go in. And I saw myself, my reflection in the window. And I thought, “I wonder who that bum is.” And then I saw it was me. Now look at me, I’m a bum. Look at me. Look at you. You’re a bum.”
—J.P. (James Pinckney)
“Now fades the lasts long streak of snow,
Now burgeons every maze of quick
About the flowering squares, and thick
By ashen roots the violets blow.”
—Alfred Tennyson (1809–1892)