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Table 4 Numerical results for Example 1

From: Twelfth degree spline with application to quadrature

x Clamped spline Not a knot spline Our spline (degree 12) Exact
1.08 0.03922071396027 0.03922071396027 0.039220713153281 0.039220713153281
1.16 0.07696103950333 0.07696102915780 0.076961041136128 0.076961041136128
1.24 0.11332868156060 0.11332867398715 0.113328685307003 0.113328685307003
1.32 0.14841999962514 0.14841999130891 0.148420005118273 0.148420005118273
1.40 0.18232154982349 0.18232154170628 0.182321556793955 0.182321556793955
1.48 0.21511137139673 0.21511136322620 0.215111379616945 0.215111379616945
1.56 0.24686006864661 0.24686006049037 0.246860077931526 0.246860077931526
1.64 0.27763172640228 0.27763171824221 0.277631736598280 0.277631736598280
1.72 0.30748468876854 0.30748468060950 0.307484699747961 0.307484699747961
1.80 0.33647222496520 0.33647221680588 0.336472236621213 0.336472236621213
1.88 0.36464310134512 0.36464309318587 0.364643113587909 0.364643113587909
1.96 0.39204207502234 0.39204206686307 0.392042087776024 0.392042087776024
2.04 0.41871032165802 0.41871031349876 0.418710334858185 0.418710334858185
2.12 0.44468580766972 0.44468579951046 0.444685821261446 0.444685821261446
2.20 0.47000361530946 0.47000360715019 0.470003629245736 0.470003629245736
2.28 0.49469622759567 0.49469621943641 0.494696241836107 0.494696241836107
2.36 0.51879377890542 0.51879377074616 0.518793793415168 0.518793793415168
2.44 0.54232427607647 0.54232426791721 0.542324290825362 0.542324290825362
2.52 0.56531379408823 0.56531378592897 0.565313809050060 0.565313809050060
2.60 0.58778664975018 0.58778664159092 0.587786664902119 0.587786664902119
2.68 0.60976555629880 0.60976554813954 0.609765571620894 0.609765571620894
2.76 0.63127176136711 0.63127175320785 0.631271776841858 0.631271776841858
2.84 0.65232517042767 0.65232516226841 0.652325186039690 0.652325186039690
2.92 0.67294445750669 0.67294444934743 0.672944473242426 0.672944473242426
3.00 0.69314716471248 0.69314715655322 0.693147180559945 0.693147180559945
3.08 0.71294979190754 0.71294978374828 0.712949807856125 0.712949807856125
3.16 0.73236787767296 0.73236786951370 0.732367893713227 0.732367893713227
3.24 0.75141607256037 0.75141606440110 0.751416088683921 0.751416088683921
3.32 0.77010820549672 0.77010819733746 0.770108221696074 0.770108221696074
3.40 0.78845734409581 0.78845733593655 0.788457360364270 0.788457360364270
3.48 0.80647584953538 0.80647584137612 0.806475865866949 0.806475865866949
3.56 0.82417542657706 0.82417541841780 0.824175442966349 0.824175442966349
3.64 0.84156716923605 0.84156716107678 0.841567185678219 0.841567185678219
3.72 0.85866160254683 0.85866159438757 0.858661619037519 0.858661619037519
3.80 0.87546872081863 0.87546871265937 0.875468737353900 0.875468737353900
3.88 0.89199802272882 0.89199801456956 0.891998039305110 0.891998039305110
3.96 0.90825854356281 0.90825853540355 0.908258560176891 0.908258560176891
4.04 0.92425888487438 0.92425887671512 0.924258901523332 0.924258901523332
4.12 0.94000724181031 0.94000723365105 0.940007258491471 0.940007258491471
4.20 0.95551142831649 0.95551142015722 0.955511445027437 0.955511445027436
4.28 0.97077890041969 0.97077889226042 0.970778917158225 0.970778917158225
4.36 0.98581677775865 0.98581676959939 0.985816794522765 0.985816794522765
4.44 1.00063186352005 1.00063185536077 1.000631880307906 1.000631880307906
4.52 1.01523066291915 1.01523065475995 1.015230679729059 1.015230679729059
4.60 1.02961940035073 1.02961939219125 1.029619417181158 1.029619417181158
4.68 1.04380403532359 1.04380402716516 1.043804052173115 1.043804052173115
4.76 1.05779027728051 1.05779026911814 1.057790294147855 1.057790294147855
4.84 1.07158359939627 1.07158359124860 1.071583616280190 1.071583616280190
4.92 1.08518925143643 1.08518924323388 1.085189268335969 1.085189268335969
5.00 1.09861227175446 1.09861226375673 1.098612288668110 1.098612288668110