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.

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