17 Solving Numerical Problems

The NUMERIC package implements some numerical (approximative) algorithms for REDUCE, based on the REDUCE rounded mode arithmetic.¹ These algorithms are implemented for standard cases:

This package implements basic algorithms of numerical analysis. These include:

• solution of algebraic equations by Newton’s method
      num_solve({sin x=cos y, x + y = 1},{x=1,y=2})

• solution of ordinary differential equations
      num_odesolve(df(y,x)=y,y=1,x=(0 .. 1), iterations=5)

• bounds of a function over an interval
      bounds(sin x+x,x=(1 .. 2));

• minimizing a function (Fletcher Reeves steepest descent)
      num_min(sin(x)+x/5, x);

• Chebyshev curve fitting
      chebyshev_fit(sin x/x,x=(1 .. 3),5);

• numerical quadrature
      num_int(sin x,x=(0 .. pi));

They should not be called for ill-conditioned problems; please use standard mathematical libraries for these.