Re: about SOLVE

From: Alec Mihailovs (alec_at_mihailovs.com)
Date: 02/26/05

  • Next message: Carl Devore: "Re: about SOLVE" 
    Date: Sat, 26 Feb 2005 22:17:40 GMT

    > The approach of using fsolve with random initial
    > points or using a series approximation to get the initial points works
    > in about a minute.

    That is a good approach in general. For this particular example, one can
    just use roots of 1 to find 20 roots in the disc,

    > tt:=time():Digits:=14:
    > s:=[seq(evalf(exp(I*k*Pi/10)),k=0..19)]:
    > sol:=[seq(fsolve(z->z^20-exp(6/10*z+1/4*z^14+15/100*z^38-1),z,complex)
    > ,z in s)]:
    > sort(sol,(x,y)->Re(x)<Re(y));

      [-0.92967788113916, -0.88290480457775 - 0.27493030452949 I,

            -0.88290480457775 + 0.27493030452949 I,

            -0.75717314939774 - 0.53486583854938 I,

            -0.75717314939774 + 0.53486583854938 I,

            -0.56790125927015 - 0.74802543767007 I,

            -0.56790125927015 + 0.74802543767007 I,

            -0.31876744421805 - 0.88531533906831 I,

            -0.31876744421805 + 0.88531533906831 I,

            -0.024217404552146 - 0.94473405164932 I,

            -0.024217404552146 + 0.94473405164932 I,

            0.27936144072755 - 0.92143429733504 I,

            0.27936144072755 + 0.92143429733504 I,

            0.54834302036656 - 0.80381795254952 I,

            0.54834302036656 + 0.80381795254952 I,

            0.77216590847663 - 0.58400116661888 I,

            0.77216590847663 + 0.58400116661888 I,

            0.93023697804313 - 0.30061772249567 I,

            0.93023697804313 + 0.30061772249567 I, 1.]

    > time()-tt;

                                    0.266

    > nops(sol);

                                      20

    Alec

  • Next message: Carl Devore: "Re: about SOLVE"

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