least_square_fit.adb
fit exp(x)*sin(x) 100 points 0.0 to Pi,   3 degree polynomial
C(   1)=  1.0348E+00
C(   2)= -4.7476E+00
C(   3)=  7.9192E+00
C(   4)= -2.0368E+00
check_pn k=100
xmin=  3.140E-02, xmax=  3.140E+00, ymin=  3.240E-02, ymax=  7.460E+00
max=  1.1126E+00 at 100, xbad=  3.140E+00, ybad=  3.680E-02
rms_err=  3.6981E-01, avg_err=  3.1762E-01, max_err=  1.1126E+00

fit exp(x)*sin(x) 100 points 0.0 to Pi,   4 degree polynomial
C(   1)= -1.8169E-01
C(   2)=  2.5957E+00
C(   3)= -2.3799E+00
C(   4)=  2.9980E+00
C(   5)= -7.9378E-01
check_pn k=100
xmin=  3.140E-02, xmax=  3.140E+00, ymin=  3.240E-02, ymax=  7.460E+00
max=  1.3484E-01 at   1, xbad=  3.140E-02, ybad=  3.240E-02
rms_err=  4.6266E-02, avg_err=  4.0140E-02, max_err=  1.3484E-01

fit exp(x)*sin(x) 100 points 0.0 to Pi,   5 degree polynomial
C(   1)= -3.8930E-03
C(   2)=  1.0234E+00
C(   3)=  1.0217E+00
C(   4)=  1.5938E-01
C(   5)=  2.1060E-01
C(   6)= -1.2668E-01
check_pn k=100
xmin=  3.140E-02, xmax=  3.140E+00, ymin=  3.240E-02, ymax=  7.460E+00
max=  1.4984E-02 at 100, xbad=  3.140E+00, ybad=  3.680E-02
rms_err=  3.4322E-03, avg_err=  2.7031E-03, max_err=  1.4984E-02

fit exp(x)*sin(x) 100 points 0.0 to Pi,   6 degree polynomial
C(   1)=  8.4252E-03
C(   2)=  8.7511E-01
C(   3)=  1.4755E+00
C(   4)= -4.0569E-01
C(   5)=  5.4279E-01
C(   6)= -2.1867E-01
C(   7)=  9.6684E-03
check_pn k=100
xmin=  3.140E-02, xmax=  3.140E+00, ymin=  3.240E-02, ymax=  7.460E+00
max=  6.8923E-03 at 100, xbad=  3.140E+00, ybad=  3.680E-02
rms_err=  2.0280E-03, avg_err=  1.7295E-03, max_err=  6.8923E-03

fit exp(x)*sin(x) 100 points 0.0 to Pi,   7 degree polynomial
C(   1)= -1.8236E-03
C(   2)=  1.0345E+00
C(   3)=  8.2486E-01
C(   4)=  7.1265E-01
C(   5)= -4.1787E-01
C(   6)=  2.1555E-01
C(   7)= -8.9041E-02
C(   8)=  8.8928E-03
check_pn k=100
xmin=  3.140E-02, xmax=  3.140E+00, ymin=  3.240E-02, ymax=  7.460E+00
max=  1.0412E-03 at 100, xbad=  3.140E+00, ybad=  3.680E-02
rms_err=  3.3924E-04, avg_err=  2.9325E-04, max_err=  1.0412E-03