Orthogonal Polynomials Approximation

数值分析，计算正交基多项式的系数

-Given a function f and a set of m >0 distinct points . You are supposed to write a function to approximate f by an orthogonal polynomial using the exact function values at the given m points with a weight　assigned to each point . The total error　must be no larger than a given tolerance.



Format of function

int OPA( double (*f)(double t), int m, double x[], double w[], double c[], double*eps )



where the function pointer double (*f)(double t) defines the function f　int m is the number of points　double x[] contains points　 double w[] contains the values of a weight function at the given points x[]　double c[] contains the coefficients　of the approximation polynomial　 double*eps is passed into the function as the tolerance for the error, and is supposed to be returned as the value of error.　The function OPA is supposed to return the degree of the approximation polynomial.



Note: a constant Max_n is defined so that if the total error is still not small enough when n = Ma