computed integrals and their error

2 files changed, 194 insertions, 0 deletions

diff --git a/res/1image_results b/res/1image_results
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+# results of numerical integration of three different functions
+# (exp, sin and some 10 degree polynomial) on [-0.5; 1] interval
+#
+#FUNC ___QUAD_TYPE POLY_ORDER SUBINTERVALS _______COMPUTED_VALUE __________VALUE_ERROR
+# function exp;  exact integral:   2.1117511687464114     
+  exp newton-cotes          0            1  1.92603812503161E+00  1.85713043714799E-01
+  exp newton-cotes          1            1  2.49360936612876E+00  3.81858197382348E-01
+  exp newton-cotes          2            1  2.11522860176938E+00  3.47743302297232E-03
+  exp newton-cotes          0            4  2.09942819014194E+00  1.23229786044705E-02
+  exp newton-cotes          1            4  2.13644044529640E+00  2.46892765499878E-02
+  exp newton-cotes          2            4  2.11176567146228E+00  1.45027158686695E-05
+  exp newton-cotes          0           16  2.11097802057075E+00  7.73148175662541E-04
+  exp newton-cotes          1           16  2.11329763497804E+00  1.54646623162780E-03
+  exp newton-cotes          2           16  2.11175128830827E+00  1.19561858191730E-07
+  exp newton-cotes          0           64  2.11170283537234E+00  4.83333740683989E-05
+  exp newton-cotes          1           64  2.11184783615831E+00  9.66674118965116E-05
+  exp newton-cotes          2           64  2.11175123190275E+00  6.31563419339898E-08
+  exp newton-cotes          0          128  2.11173908525770E+00  1.20834887136212E-05
+  exp newton-cotes          1          128  2.11177533576533E+00  2.41670189140564E-05
+  exp newton-cotes          2          128  2.11175123169533E+00  6.29489180781206E-08
+  exp        gauss          1            1  1.92603812503161E+00  1.85713043714799E-01
+  exp        gauss          2            1  2.10944323004618E+00  2.30793870023227E-03
+  exp        gauss          3            1  2.11174017498829E+00  1.09937581247443E-05
+  exp        gauss          1            4  2.09942819014194E+00  1.23229786044705E-02
+  exp        gauss          2            4  2.11174154446915E+00  9.62427726047821E-06
+  exp        gauss          3            4  2.11175122970046E+00  6.09540506957273E-08
+  exp        gauss          1           16  2.11097802057075E+00  7.73148175662541E-04
+  exp        gauss          2           16  2.11175113096814E+00  3.77782729543696E-08
+  exp        gauss          3           16  2.11175123173832E+00  6.29919068018125E-08
+  exp        gauss          1           64  2.11170283537234E+00  4.83333740683989E-05
+  exp        gauss          2           64  2.11175116859717E+00  1.49236623059323E-10
+  exp        gauss          3           64  2.11175123168510E+00  6.29386853745473E-08
+  exp        gauss          1          128  2.11173908525770E+00  1.20834887136212E-05
+  exp        gauss          2          128  2.11175116873676E+00  9.65227897609111E-12
+  exp        gauss          3          128  2.11175123168240E+00  6.29359884207759E-08
+# function sin;  exact integral:  0.33728025602223299     
+  sin newton-cotes          0            1  3.71105938881784E-01  3.38256828595514E-02
+  sin newton-cotes          1            1  2.71534084652770E-01  6.57461713694629E-02
+  sin newton-cotes          2            1  3.37915330876108E-01  6.35074853874595E-04
+  sin newton-cotes          0            4  3.39264643397494E-01  1.98438737526069E-03
+  sin newton-cotes          1            4  3.33318458216852E-01  3.96179780538147E-03
+  sin newton-cotes          2            4  3.37282591722417E-01  2.33570018431939E-06
+  sin newton-cotes          0           16  3.37403803411294E-01  1.23547389060619E-04
+  sin newton-cotes          1           16  3.37033188390897E-01  2.47067631336084E-04
+  sin newton-cotes          2           16  3.37280275122897E-01  1.91006635508195E-08
+  sin newton-cotes          0           64  3.37287975878341E-01  7.71985610759085E-06
+  sin newton-cotes          1           64  3.37264816416034E-01  1.54396061991524E-05
+  sin newton-cotes          2           64  3.37280266109307E-01  1.00870736763348E-08
+  sin newton-cotes          0          128  3.37282185963069E-01  1.92994083580977E-06
+  sin newton-cotes          1          128  3.37276396147187E-01  3.85987504569751E-06
+  sin newton-cotes          2          128  3.37280266076177E-01  1.00539435665681E-08
+  sin        gauss          1            1  3.71105938881784E-01  3.38256828595514E-02
+  sin        gauss          2            1  3.36854984312796E-01  4.25271709437014E-04
+  sin        gauss          3            1  3.37282324636480E-01  2.06861424700833E-06
+  sin        gauss          1            4  3.39264643397494E-01  1.98438737526069E-03
+  sin        gauss          2            4  3.37278705228509E-01  1.55079372354816E-06
+  sin        gauss          3            4  3.37280266394011E-01  1.03717775479240E-08
+  sin        gauss          1           16  3.37403803411294E-01  1.23547389060619E-04
+  sin        gauss          2           16  3.37280249993944E-01  6.02828925666543E-09
+  sin        gauss          3           16  3.37280266064890E-01  1.00426572058332E-08
+  sin        gauss          1           64  3.37287975878341E-01  7.71985610759085E-06
+  sin        gauss          2           64  3.37280255998951E-01  2.32820429602043E-11
+  sin        gauss          3           64  3.37280266073394E-01  1.00511605705123E-08
+  sin        gauss          1          128  3.37282185963069E-01  1.92994083580977E-06
+  sin        gauss          2          128  3.37280256020830E-01  1.40315536967250E-12
+  sin        gauss          3          128  3.37280266073824E-01  1.00515913370458E-08
+# function poly;  exact integral:  -6.4224397408682314     
+ poly newton-cotes          0            1 -1.04998702415752E+01  4.07743050070696E+00
+ poly newton-cotes          1            1 -1.97724531433778E+00  4.44519442653045E+00
+ poly newton-cotes          2            1 -7.65899549408524E+00  1.23655575321700E+00
+ poly newton-cotes          0            4 -6.36528927667174E+00  5.71504641964946E-02
+ poly newton-cotes          1            4 -6.62002771387664E+00  1.97587973008410E-01
+ poly newton-cotes          2            4 -6.45020228130437E+00  2.77625404361412E-02
+ poly newton-cotes          0           16 -6.41314392114169E+00  9.29581972654514E-03
+ poly newton-cotes          1           16 -6.44138433706261E+00  1.89445961943822E-02
+ poly newton-cotes          2           16 -6.42255758452246E+00  1.17843654225069E-04
+ poly newton-cotes          0           64 -6.42183460280302E+00  6.05138065211008E-04
+ poly newton-cotes          1           64 -6.42365136575042E+00  1.21162488218474E-03
+ poly newton-cotes          2           64 -6.42244038185579E+00  6.40987554589856E-07
+ poly newton-cotes          0          128 -6.42228814404890E+00  1.51596819327970E-04
+ poly newton-cotes          1          128 -6.42274298427672E+00  3.03243408486864E-04
+ poly newton-cotes          2          128 -6.42243994886180E+00  2.07993563705600E-07
+ poly        gauss          1            1 -1.04998702415752E+01  4.07743050070696E+00
+ poly        gauss          2            1 -5.84748222218842E+00  5.74957518679808E-01
+ poly        gauss          3            1 -6.18128177279518E+00  2.41157968073056E-01
+ poly        gauss          1            4 -6.36528927667174E+00  5.71504641964946E-02
+ poly        gauss          2            4 -6.40404341324466E+00  1.83963276235755E-02
+ poly        gauss          3            4 -6.42231899648526E+00  1.20744382967608E-04
+ poly        gauss          1           16 -6.41314392114169E+00  9.29581972654514E-03
+ poly        gauss          2           16 -6.42236131242383E+00  7.84284444055316E-05
+ poly        gauss          3           16 -6.42243989131854E+00  1.50450309988059E-07
+ poly        gauss          1           64 -6.42183460280302E+00  6.05138065211008E-04
+ poly        gauss          2           64 -6.42243942065755E+00  3.20210681969968E-07
+ poly        gauss          3           64 -6.42243992002596E+00  1.79157725099799E-07
+ poly        gauss          1          128 -6.42228814404890E+00  1.51596819327970E-04
+ poly        gauss          2          128 -6.42243970932995E+00  3.15382813198539E-08
+ poly        gauss          3          128 -6.42243991999923E+00  1.79130998922972E-07
diff --git a/res/5images_results b/res/5images_results
new file mode 100644
index 0000000..b130ade
--- /dev/null
+++ b/res/5images_results
@@ -0,0 +1,97 @@
+# results of numerical integration of three different functions
+# (exp, sin and some 10 degree polynomial) on [-0.5; 1] interval
+#
+#FUNC ___QUAD_TYPE POLY_ORDER SUBINTERVALS _______COMPUTED_VALUE __________VALUE_ERROR
+# function exp;  exact integral:   2.1117511687464114     
+  exp newton-cotes          0            1  1.92603812503161E+00  1.85713043714799E-01
+  exp newton-cotes          1            1  2.49360936612876E+00  3.81858197382348E-01
+  exp newton-cotes          2            1  2.11522860176938E+00  3.47743302297232E-03
+  exp newton-cotes          0            4  2.09942819014194E+00  1.23229786044705E-02
+  exp newton-cotes          1            4  2.13644044529640E+00  2.46892765499878E-02
+  exp newton-cotes          2            4  2.11176567146228E+00  1.45027158686695E-05
+  exp newton-cotes          0           16  2.11097802057075E+00  7.73148175662541E-04
+  exp newton-cotes          1           16  2.11329763497804E+00  1.54646623162780E-03
+  exp newton-cotes          2           16  2.11175128830827E+00  1.19561858191730E-07
+  exp newton-cotes          0           64  2.11170283537234E+00  4.83333740683989E-05
+  exp newton-cotes          1           64  2.11184783615831E+00  9.66674118965116E-05
+  exp newton-cotes          2           64  2.11175123190275E+00  6.31563419339898E-08
+  exp newton-cotes          0          128  2.11173908525770E+00  1.20834887136212E-05
+  exp newton-cotes          1          128  2.11177533576533E+00  2.41670189140564E-05
+  exp newton-cotes          2          128  2.11175123169533E+00  6.29489180781206E-08
+  exp        gauss          1            1  1.92603812503161E+00  1.85713043714799E-01
+  exp        gauss          2            1  2.10944323004618E+00  2.30793870023227E-03
+  exp        gauss          3            1  2.11174017498829E+00  1.09937581247443E-05
+  exp        gauss          1            4  2.09942819014194E+00  1.23229786044705E-02
+  exp        gauss          2            4  2.11174154446915E+00  9.62427726047821E-06
+  exp        gauss          3            4  2.11175122970046E+00  6.09540506957273E-08
+  exp        gauss          1           16  2.11097802057075E+00  7.73148175662541E-04
+  exp        gauss          2           16  2.11175113096814E+00  3.77782729543696E-08
+  exp        gauss          3           16  2.11175123173832E+00  6.29919063577233E-08
+  exp        gauss          1           64  2.11170283537234E+00  4.83333740683989E-05
+  exp        gauss          2           64  2.11175116859718E+00  1.49236178970114E-10
+  exp        gauss          3           64  2.11175123168510E+00  6.29386858186365E-08
+  exp        gauss          1          128  2.11173908525770E+00  1.20834887136212E-05
+  exp        gauss          2          128  2.11175116873676E+00  9.65227897609111E-12
+  exp        gauss          3          128  2.11175123168240E+00  6.29359884207759E-08
+# function sin;  exact integral:  0.33728025602223299     
+  sin newton-cotes          0            1  3.71105938881784E-01  3.38256828595514E-02
+  sin newton-cotes          1            1  2.71534084652770E-01  6.57461713694629E-02
+  sin newton-cotes          2            1  3.37915330876108E-01  6.35074853874595E-04
+  sin newton-cotes          0            4  3.39264643397494E-01  1.98438737526074E-03
+  sin newton-cotes          1            4  3.33318458216852E-01  3.96179780538142E-03
+  sin newton-cotes          2            4  3.37282591722417E-01  2.33570018426388E-06
+  sin newton-cotes          0           16  3.37403803411294E-01  1.23547389060674E-04
+  sin newton-cotes          1           16  3.37033188390897E-01  2.47067631336084E-04
+  sin newton-cotes          2           16  3.37280275122897E-01  1.91006635508195E-08
+  sin newton-cotes          0           64  3.37287975878341E-01  7.71985610764636E-06
+  sin newton-cotes          1           64  3.37264816416034E-01  1.54396061991524E-05
+  sin newton-cotes          2           64  3.37280266109307E-01  1.00870736208236E-08
+  sin newton-cotes          0          128  3.37282185963069E-01  1.92994083586528E-06
+  sin newton-cotes          1          128  3.37276396147187E-01  3.85987504569751E-06
+  sin newton-cotes          2          128  3.37280266076177E-01  1.00539435665681E-08
+  sin        gauss          1            1  3.71105938881784E-01  3.38256828595514E-02
+  sin        gauss          2            1  3.36854984312796E-01  4.25271709437014E-04
+  sin        gauss          3            1  3.37282324636480E-01  2.06861424700833E-06
+  sin        gauss          1            4  3.39264643397494E-01  1.98438737526074E-03
+  sin        gauss          2            4  3.37278705228509E-01  1.55079372360367E-06
+  sin        gauss          3            4  3.37280266394011E-01  1.03717775479240E-08
+  sin        gauss          1           16  3.37403803411294E-01  1.23547389060674E-04
+  sin        gauss          2           16  3.37280249993944E-01  6.02828925666543E-09
+  sin        gauss          3           16  3.37280266064890E-01  1.00426572058332E-08
+  sin        gauss          1           64  3.37287975878341E-01  7.71985610764636E-06
+  sin        gauss          2           64  3.37280255998951E-01  2.32820429602043E-11
+  sin        gauss          3           64  3.37280266073394E-01  1.00511605705123E-08
+  sin        gauss          1          128  3.37282185963069E-01  1.92994083586528E-06
+  sin        gauss          2          128  3.37280256020830E-01  1.40309985852127E-12
+  sin        gauss          3          128  3.37280266073824E-01  1.00515913370458E-08
+# function poly;  exact integral:  -6.4224397408682314     
+ poly newton-cotes          0            1 -1.04998702415752E+01  4.07743050070696E+00
+ poly newton-cotes          1            1 -1.97724531433778E+00  4.44519442653045E+00
+ poly newton-cotes          2            1 -7.65899549408524E+00  1.23655575321700E+00
+ poly newton-cotes          0            4 -6.36528927667174E+00  5.71504641964937E-02
+ poly newton-cotes          1            4 -6.62002771387664E+00  1.97587973008409E-01
+ poly newton-cotes          2            4 -6.45020228130437E+00  2.77625404361412E-02
+ poly newton-cotes          0           16 -6.41314392114169E+00  9.29581972654425E-03
+ poly newton-cotes          1           16 -6.44138433706261E+00  1.89445961943822E-02
+ poly newton-cotes          2           16 -6.42255758452246E+00  1.17843654224181E-04
+ poly newton-cotes          0           64 -6.42183460280302E+00  6.05138065209232E-04
+ poly newton-cotes          1           64 -6.42365136575041E+00  1.21162488218296E-03
+ poly newton-cotes          2           64 -6.42244038185579E+00  6.40987553701677E-07
+ poly newton-cotes          0          128 -6.42228814404890E+00  1.51596819328859E-04
+ poly newton-cotes          1          128 -6.42274298427672E+00  3.03243408486864E-04
+ poly newton-cotes          2          128 -6.42243994886180E+00  2.07993564593778E-07
+ poly        gauss          1            1 -1.04998702415752E+01  4.07743050070696E+00
+ poly        gauss          2            1 -5.84748222218842E+00  5.74957518679808E-01
+ poly        gauss          3            1 -6.18128177279518E+00  2.41157968073056E-01
+ poly        gauss          1            4 -6.36528927667174E+00  5.71504641964937E-02
+ poly        gauss          2            4 -6.40404341324466E+00  1.83963276235755E-02
+ poly        gauss          3            4 -6.42231899648526E+00  1.20744382966720E-04
+ poly        gauss          1           16 -6.41314392114169E+00  9.29581972654425E-03
+ poly        gauss          2           16 -6.42236131242383E+00  7.84284444055316E-05
+ poly        gauss          3           16 -6.42243989131854E+00  1.50450309988059E-07
+ poly        gauss          1           64 -6.42183460280302E+00  6.05138065209232E-04
+ poly        gauss          2           64 -6.42243942065755E+00  3.20210682858146E-07
+ poly        gauss          3           64 -6.42243992002596E+00  1.79157725099799E-07
+ poly        gauss          1          128 -6.42228814404890E+00  1.51596819328859E-04
+ poly        gauss          2          128 -6.42243970932995E+00  3.15382804316755E-08
+ poly        gauss          3          128 -6.42243991999923E+00  1.79130998922972E-07