Biconjugate gradient method

In mathematics, more specifically in numerical linear algebra, the biconjugate gradient method is an algorithm to solve systems of linear equations

Unlike the conjugate gradient method, this algorithm does not require the matrix ${\displaystyle A}$ to be self-adjoint, but instead one needs to perform multiplications by the conjugate transpose A^*.

In the above formulation, the computed ${\displaystyle r_{k}\,}$ and ${\displaystyle r_{k}^{*}}$ satisfy

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