ÂQÂDªÂðÂÂÂÃÂé (Root finding) FindRoot[] Of course, the square root function is built into Mathematica, so it is not necessary to use FindRoot[] to compute the square root of 2, but it provides a good example illustrating some aspects of the function.  ½ÂèÂæÂÃ
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ÂAÂQÂýÂûªÂðÂÂÂÃÂéÂÃÂÃFindRootÂðÂg¤ÂKÂvÂàÂèÂùÂñÂBµ©µÂAÂúÂÃÂáÂñÂÃÂêÂÃÂÃÂæ¤ÂÃÂgÂÃÂêÂé©Âð¦·Âæ¢ÂïÂÃÂáÂÃÂÃÂèÂ÷ÂB The command above used Newton's method. This is the best method to use when the derivative of the function can be computed directly. Sometimes this is not possible, in which case it is best to use the secant method (Brent's method in 1D if the root is bracketed). This is done by specifying two starting points for the algorithm. The root is reasonably accurate: «ÂÃÂÃ
«Â鸧ÂÃÂÂÂlª¾ÂçÂêÂõ½ÂB x^2 /. % Suppose you wanted to know how many digits of the root were correct. This is easy to do in Mathematica by using bignums. In FindRoot (and most other numerical functions as well), the precision of numbers used is controlled by the option WorkingPrecision. For example, to work with 32 digits, you can use Âà µÂA±ÂýÂûªÂøÂxÂðÂmÂè½¢ÂêÂÂÂÃbignumsÂðÂg¤±ÂêÂÃ
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Âg¤ÂÂÂÃÂÂÂÃÂæ¤ÂÃÂwÂèµÂ÷ÂB two = x^2 /. % | |
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