Mathematica: Parabolic Fit using Predefined Program and ErrorBarPlots Module

[Hoiya]

I'm using a predefinied program... but I don't know because give me this error:

Clear["Global`*"]

Remove["Global`*"]

<< "ErrorBarPlots`"


xdata = {180, 200, 220, 240, 260, 280, 300, 320, 340, 360}

{180, 200, 220, 240, 260, 280, 300, 320, 340, 360}


ax = First[xdata]

180

bx = Last[xdata]

360

apx = 2./(bx - ax)

0.0111111

bpx = (bx + ax)/(bx - ax)

3

xdata1 = xdata*apx - bpx

{-1., -0.777778, -0.555556, -0.333333, -0.111111, 0.111111, 0.333333, \
0.555556, 0.777778, 1.}


xdata1 = xdata

{180, 200, 220, 240, 260, 280, 300, 320, 340, 360}


ydata1 = {13.8, 16.3, 18.2, 19.7, 20.4, 20.4, 19.8, 18.7, 17, 15}

{13.8, 16.3, 18.2, 19.7, 20.4, 20.4, 19.8, 18.7, 17, 15}


s = {0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1}

{0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1}


numpt = 10

10


matD = {{Sum[1/(s[])^2, {i, numpt}],
Sum[xdata1[]/(s[])^2, {i, numpt}],
Sum[(xdata1[])^2/(s[])^2, {i, numpt}]}, {Sum[
xdata1[]/(s[])^2, {i, numpt}],
Sum[(xdata1[])^2/(s[])^2, {i, numpt}],
Sum[(xdata1[])^3/(s[])^2, {i,
numpt}]}, {Sum[(xdata1[])^2/(s[])^2, {i, numpt}],
Sum[(xdata1[])^3/(s[])^2, {i, numpt}],
Sum[(xdata1[])^4/(s[])^2, {i, numpt}]}}

{{999.9999999999999`, 269999.99999999994`,
7.619999999999999`*^7}, {269999.99999999994`, 7.619999999999999`*^7,
2.2355999999999996`*^10}, {7.619999999999999`*^7,
2.2355999999999996`*^10, 6.777167999999999`*^12}}

MatrixForm[matD]

\!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"999.9999999999999`", "269999.99999999994`", "7.619999999999999`*^7"},
{"269999.99999999994`", "7.619999999999999`*^7",
"2.2355999999999996`*^10"},
{"7.619999999999999`*^7", "2.2355999999999996`*^10",
"6.777167999999999`*^12"}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {},
"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]},
Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
Offset[0.2], {
Offset[0.4]},
Offset[0.2]}, "RowsIndexed" -> {}}], "", ")"}],
Function[BoxForm`e$,
MatrixForm[BoxForm`e$]]]\)


matDinver = Inverse[matD]

Inverse::luc: Result for Inverse of badly conditioned matrix {{1000.,270000.,7.62*10^7},{270000.,7.62*10^7,2.2356*10^10},{7.62*10^7,2.2356*10^10,6.77717*10^12}} may contain significant numerical errors. >>

{{0.5965, -0.00453068, 8.23864*10^-6}, {-0.00453068,
0.0000348201, -6.39205*10^-8}, {8.23864*10^-6, -6.39205*10^-8,
1.18371*10^-10}}

can anybody help me?

 

[Dale]

If you do SingularValueList[matD] you see that your largest singular value is 6.8E12 and the smallest is 1.7E0. So a matrix inversion can be expected to lose about 12 digits of precision. This isn't an issue with Mathematica, it is a feature of the matrix itself.