Inverting a Linear Fractional Transformation

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I have a particular Linear Fractional Transformation from $mathbbC$ to $mathbbC$, I am using to solve Laplace's equation, and I was hoping to find the inverse of this transformation. Is there a algorithm that can be used to find the inverse of a Linear Fractional Transformation? Are there any useful algorithms for special cases?




complex-analysis inverse mobius-transformation




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    I have a particular Linear Fractional Transformation from $mathbbC$ to $mathbbC$, I am using to solve Laplace's equation, and I was hoping to find the inverse of this transformation. Is there a algorithm that can be used to find the inverse of a Linear Fractional Transformation? Are there any useful algorithms for special cases?




    complex-analysis inverse mobius-transformation




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      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      I have a particular Linear Fractional Transformation from $mathbbC$ to $mathbbC$, I am using to solve Laplace's equation, and I was hoping to find the inverse of this transformation. Is there a algorithm that can be used to find the inverse of a Linear Fractional Transformation? Are there any useful algorithms for special cases?




      complex-analysis inverse mobius-transformation




      share|cite|improve this question














      I have a particular Linear Fractional Transformation from $mathbbC$ to $mathbbC$, I am using to solve Laplace's equation, and I was hoping to find the inverse of this transformation. Is there a algorithm that can be used to find the inverse of a Linear Fractional Transformation? Are there any useful algorithms for special cases?





      complex-analysis inverse mobius-transformation





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      edited May 7 '17 at 3:26

























      asked May 7 '17 at 2:54









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          2 Answers
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          The inverse of the linear fractional transformation
          $$zto fraca z + bc z + d$$ is the linear fractional transformation
          $$zto frace z + fg z + h$$ where the matrix
          $$beginpmatrixe & f\ g & hendpmatrix$$ is the inverse of the matrix
          $$beginpmatrixa & b\ c & dendpmatrix.$$






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          • don't even need to divide through by determinant...
            – Will Jagy
            May 7 '17 at 3:00

















          up vote
          -1
          down vote













          Answer is here:



          https://ieeexplore.ieee.org/document/7106488/



          There is a simple expression to compute the inverse LFT...






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          • While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes
            – Siong Thye Goh
            Aug 19 at 3:28










          Your Answer




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          2 Answers
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          active

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          2 Answers
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          active

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          active

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          up vote
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          The inverse of the linear fractional transformation
          $$zto fraca z + bc z + d$$ is the linear fractional transformation
          $$zto frace z + fg z + h$$ where the matrix
          $$beginpmatrixe & f\ g & hendpmatrix$$ is the inverse of the matrix
          $$beginpmatrixa & b\ c & dendpmatrix.$$






          share|cite|improve this answer




















          • don't even need to divide through by determinant...
            – Will Jagy
            May 7 '17 at 3:00














          up vote
          1
          down vote













          The inverse of the linear fractional transformation
          $$zto fraca z + bc z + d$$ is the linear fractional transformation
          $$zto frace z + fg z + h$$ where the matrix
          $$beginpmatrixe & f\ g & hendpmatrix$$ is the inverse of the matrix
          $$beginpmatrixa & b\ c & dendpmatrix.$$






          share|cite|improve this answer




















          • don't even need to divide through by determinant...
            – Will Jagy
            May 7 '17 at 3:00












          up vote
          1
          down vote










          up vote
          1
          down vote









          The inverse of the linear fractional transformation
          $$zto fraca z + bc z + d$$ is the linear fractional transformation
          $$zto frace z + fg z + h$$ where the matrix
          $$beginpmatrixe & f\ g & hendpmatrix$$ is the inverse of the matrix
          $$beginpmatrixa & b\ c & dendpmatrix.$$






          share|cite|improve this answer












          The inverse of the linear fractional transformation
          $$zto fraca z + bc z + d$$ is the linear fractional transformation
          $$zto frace z + fg z + h$$ where the matrix
          $$beginpmatrixe & f\ g & hendpmatrix$$ is the inverse of the matrix
          $$beginpmatrixa & b\ c & dendpmatrix.$$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered May 7 '17 at 2:59









          Igor Rivin

          15.9k11134




          15.9k11134











          • don't even need to divide through by determinant...
            – Will Jagy
            May 7 '17 at 3:00
















          • don't even need to divide through by determinant...
            – Will Jagy
            May 7 '17 at 3:00















          don't even need to divide through by determinant...
          – Will Jagy
          May 7 '17 at 3:00




          don't even need to divide through by determinant...
          – Will Jagy
          May 7 '17 at 3:00










          up vote
          -1
          down vote













          Answer is here:



          https://ieeexplore.ieee.org/document/7106488/



          There is a simple expression to compute the inverse LFT...






          share|cite|improve this answer




















          • While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes
            – Siong Thye Goh
            Aug 19 at 3:28














          up vote
          -1
          down vote













          Answer is here:



          https://ieeexplore.ieee.org/document/7106488/



          There is a simple expression to compute the inverse LFT...






          share|cite|improve this answer




















          • While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes
            – Siong Thye Goh
            Aug 19 at 3:28












          up vote
          -1
          down vote










          up vote
          -1
          down vote









          Answer is here:



          https://ieeexplore.ieee.org/document/7106488/



          There is a simple expression to compute the inverse LFT...






          share|cite|improve this answer












          Answer is here:



          https://ieeexplore.ieee.org/document/7106488/



          There is a simple expression to compute the inverse LFT...







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 19 at 3:06









          Moises Ferber

          1




          1











          • While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes
            – Siong Thye Goh
            Aug 19 at 3:28
















          • While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes
            – Siong Thye Goh
            Aug 19 at 3:28















          While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes
          – Siong Thye Goh
          Aug 19 at 3:28




          While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes
          – Siong Thye Goh
          Aug 19 at 3:28












           

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