Description:

• dirtyinfnorm(f,I) computes an approximation of the infinity norm of the given function f on the interval I, e.g. max {|f(x)|, x in I}.
• The interval must be bound. If the interval contains one of -Inf or +Inf, the result of dirtyinfnorm is NaN.
• The result of this command depends on the global variables prec and points. Therefore, the returned result is generally a good approximation of the exact infinity norm, with precision prec. However, the result is generally underestimated and should not be used when safety is critical. Use infnorm instead.
• The following algorithm is used: let n be the value of variable points and t be the value of variable prec.
  • Evaluate |f| at n evenly distributed points in the interval I. The evaluation are faithful roundings of the exact results at precision t.
  • Whenever the derivative of f changes its sign for two consecutive points, find an approximation x of its zero with precision t. Then compute a faithful rounding of |f(x)| at precision t.
  • Return the maximum of all computed values.