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ExampleSystems :: quadgrid

quadgrid -- interpolating quadrature formula for function defined on a grid

Synopsis

Description

This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.

There were 5 solutions found in 1.653 seconds (with a Bezout bound of 120).

Note: This system is ill-conditioned. There are 4 complex and 1 real solution.

Reference: "The construction and application of wavelets in numerical analysis" by Wim Sweldens.

See also: http://homepages.math.uic.edu/~jan/Demo/quadgrid.html.

i1 : quadgrid(RR_53)

                                                                                     2      2      2      2                      
o1 = {w  + w  + w  + w  - 1, w b + w b + w b + w b + .5w  + w  + 1.5w  - .633975, w b  + w b  + w b  + w b  + w b + 2w b + 3w b +
       0    1    2    3       0     1     2     3       1    2       3             0      1      2      3      1      2      3   
     ----------------------------------------------------------------------------------------------------------------------------
                                      3      3      3      3         2       2         2                                        
     .25w  + w  + 4.5w  - .401924, w b  + w b  + w b  + w b  + 1.5w b  + 3w b  + 4.5w b  + .75w b + 3w b + 6.75w b + .125w  + w 
         1    2       3             0      1      2      3         1       2         3         1      2         3         1    2
     ----------------------------------------------------------------------------------------------------------------------------
                             4      4      4      4       3       3       3         2       2          2
     + 3.375w  - .131092, w b  + w b  + w b  + w b  + 2w b  + 4w b  + 6w b  + 1.5w b  + 6w b  + 13.5w b  + .5w b + 4w b + 13.5w b
             3             0      1      2      3       1       2       3         1       2          3        1      2         3 
     ----------------------------------------------------------------------------------------------------------------------------
     + .0625w  + w  + 5.0625w  + .302193}
             1    2          3

o1 : List

Ways to use quadgrid :

For the programmer

The object quadgrid is a method function.