@article{Hoeven:2019aa,
    Abstract = {The technique of relaxed power series expansion provides an efficient way to solve so called recursive equations of the form {\$}{\$}F = {$\backslash$}varPhi (F){\$}{\$}, where the unknown F is a vector of power series, and where the solution can be obtained as the limit of the sequence {\$}{\$}0, {$\backslash$}varPhi (0), {$\backslash$}varPhi ({$\backslash$}varPhi (0)), {$\backslash$}ldots {\$}{\$}. With respect to other techniques, such as Newton's method, two major advantages are its generality and the fact that it takes advantage of possible sparseness of {\$}{\$}{$\backslash$}varPhi {\$}{\$}. In this paper, we consider more general implicit equations of the form {\$}{\$}{$\backslash$}varPhi (F) = 0{\$}{\$}. Under mild assumptions on such an equation, we will show that it can be rewritten as a recursive equation.},
    Author = {van der Hoeven, Joris},
    Date = {2019/06/01},
    File = {From implicit to recursive equations - 10.1007@s00200-018-0370-2 - a - a.pdf},
    ISBN = {1432-0622},
    Journal = {Applicable Algebra in Engineering, Communication and Computing},
    Number = {3},
    Pages = {243--262},
    Title = {From implicit to recursive equations},
    URL = {https://doi.org/10.1007/s00200-018-0370-2},
    Volume = {30},
    Year = {2019},
    bdsk-url-1 = {https://doi.org/10.1007/s00200-018-0370-2},
    date-added = {2023-02-02 22:15:28 +0100},
    date-modified = {2023-02-02 22:15:28 +0100},
    id = {van der Hoeven2019},
    doi = {10.1007/s00200-018-0370-2}
}

@article{Hoeven:2019aa, Abstract = {The technique of relaxed power series expansion provides an efficient way to solve so called recursive equations of the form {\$}{\$}F = {$\backslash$}varPhi (F){\$}{\$}, where the unknown F is a vector of power series, and where the solution can be obtained as the limit of the sequence {\$}{\$}0, {$\backslash$}varPhi (0), {$\backslash$}varPhi ({$\backslash$}varPhi (0)), {$\backslash$}ldots {\$}{\$}. With respect to other techniques, such as Newton's method, two major advantages are its generality and the fact that it takes advantage of possible sparseness of {\$}{\$}{$\backslash$}varPhi {\$}{\$}. In this paper, we consider more general implicit equations of the form {\$}{\$}{$\backslash$}varPhi (F) = 0{\$}{\$}. Under mild assumptions on such an equation, we will show that it can be rewritten as a recursive equation.}, Author = {van der Hoeven, Joris}, Date = {2019/06/01}, File = {From implicit to recursive equations - 10.1007@s00200-018-0370-2 - a - a.pdf}, ISBN = {1432-0622}, Journal = {Applicable Algebra in Engineering, Communication and Computing}, Number = {3}, Pages = {243--262}, Title = {From implicit to recursive equations}, URL = {https://doi.org/10.1007/s00200-018-0370-2}, Volume = {30}, Year = {2019}, bdsk-url-1 = {https://doi.org/10.1007/s00200-018-0370-2}, date-added = {2023-02-02 22:15:28 +0100}, date-modified = {2023-02-02 22:15:28 +0100}, id = {van der Hoeven2019}, doi = {10.1007/s00200-018-0370-2} }