least_square_fit.java
fit exp(x)*sin(x) 100 points 0.0 to Pi, 3 degree polynomial
C[0]=1.0348073158169844
C[1]=-4.7476108162511075
C[2]=7.919246857533574
C[3]=-2.0368290368715276
check_pn k=100, xmin=0.0314, xmax=3.1399999999999997, ymin=0.03239627868648665, ymax=7.460477903091581
max=1.1126357725049327 at i=100, xbad=3.1399999999999997, ybad=0.03679644093467751
rms_err=0.36980531049037657, avg_err=0.31762423108773263, max_err=1.1126357725049327
 
fit exp(x)*sin(x) 100 points 0.0 to Pi, 4 degree polynomial
C[0]=-0.1816941512220971
C[1]=2.595707462086761
C[2]=-2.379894454617519
C[3]=2.997956694072744
C[4]=-0.793779676316682
check_pn k=100, xmin=0.0314, xmax=3.1399999999999997, ymin=0.03239627868648665, ymax=7.460477903091581
max=0.1348396538093507 at i=1, xbad=0.0314, ybad=0.03239627868648665
rms_err=0.04626577814986628, avg_err=0.04014016564637597, max_err=0.1348396538093507
 
fit exp(x)*sin(x) 100 points 0.0 to Pi, 5 degree polynomial
C[0]=-0.003892950298335418
C[1]=1.0234290926697998
C[2]=1.0217009008148223
C[3]=0.1593800823761904
C[4]=0.21059698463303156
C[5]=-0.12667927867129292
check_pn k=100, xmin=0.0314, xmax=3.1399999999999997, ymin=0.03239627868648665, ymax=7.460477903091581
max=0.014983530616147395 at i=100, xbad=3.1399999999999997, ybad=0.03679644093467751
rms_err=0.00343216208830362, avg_err=0.0027031387966933128, max_err=0.014983530616147395
 
fit exp(x)*sin(x) 100 points 0.0 to Pi, 6 degree polynomial
C[0]=0.008425217439801853
C[1]=0.8751114115126891
C[2]=1.4754832927975376
C[3]=-0.4056924894322509
C[4]=0.5427914121534629
C[5]=-0.2186660126760847
C[6]=0.00966836244892145
check_pn k=100, xmin=0.0314, xmax=3.1399999999999997, ymin=0.03239627868648665, ymax=7.460477903091581
max=0.006892300794877078 at i=100, xbad=3.1399999999999997, ybad=0.03679644093467751
rms_err=0.0020280238363087253, avg_err=0.0017294743330854801, max_err=0.006892300794877078
 
fit exp(x)*sin(x) 100 points 0.0 to Pi, 7 degree polynomial
C[0]=-0.0018235633105378006
C[1]=1.0345201729900018
C[2]=0.8248614266090878
C[3]=0.7126475421179289
C[4]=-0.41786980703147303
C[5]=0.21554759554474448
C[6]=-0.08904136786912674
C[7]=0.00889284862126615
check_pn k=100, xmin=0.0314, xmax=3.1399999999999997, ymin=0.03239627868648665, ymax=7.460477903091581
max=0.0010411699944284578 at i=100, xbad=3.1399999999999997, ybad=0.03679644093467751
rms_err=3.392393129772561E-4, avg_err=2.932511061400951E-4, max_err=0.0010411699944284578