Newton’s Method Coding

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• Questions?
  • Piecewise function for Newton lab?
    • Can’t define it anonymously, but can define it in a “.m” file:
      

      function [ y ] = piecewise( x )
      if x < 0
          y = x;
      else
          y = 2 * x;
      end

    • Then in command window can do...
      

      >> f = @(x)2*x;
      >> f(4)
      ans =
           8
      >> g = @(x)if x < 0 x else 2 * x end;
       g = @(x)if x < 0 x else 2 * x end;
               |
      {Error: Illegal use of reserved keyword "if".
      } 
      >> piecewise( -3 )
      ans =
          -3
      >> g = @piecewise;
      >> g( -3 )
      ans =
          -3

• If Statements
  • Sections 4.1 - 4.3
    • Choose whether statement or group is executed
    • Looks like
      

      if condition
          action
      end

    • Action = statement(s) to execute if condition true
    • False = 0, true = non-0
    • If-else chooses between 2 actions
      

      if condition
          action1
      else
          action2
      end

    • Nested if statements inside others
      • Choose between multiple statements
      • if-elseif
• Code Newton Lab
  • Finding square root of n with Newton’s method
    • f(x) = 0 when x = √n
    • f(x) = x² - n
    • aka x * x - n
    • Challenge (extra credit): find 1/n using Newton’s method
• Next
  • Finish Newton lab

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