Similarly, the QR decomposition expresses A as QR with Q an orthogonal matrix and R an upper triangular matrix. The system Q ( Rx ) = b is solved by Rx = Q T b = c , and the system Rx = c is solved by ' back substitution '. The number of additions and multiplications required is about twice that of using the LU solver, but no more digits are required in inexact arithmetic because the QR decomposition is numerically stable .
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