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

Synopsis

Usage:

quadgrid(kk)
Inputs:
- kk, a ring, the coefficient ring
Outputs:
- a list, of polynomials in the system

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)

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

o1 : List

Ways to use quadgrid :

quadgrid(Ring)

For the programmer

The object quadgrid is a method function.