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The QR Algorithm - ETH Z

The QR Algorithm - ETH Z

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64 CHAPTER4. THEQRALGORITHM Algorithm 4.1 Basic QR algorithm 1: Let A∈Cn×n.This algorithm computes an upper triangular matrix Tand a unitary matrix Usuch that A= UTU∗ is the Schur decomposition of A. 2: Set A0:= Aand U0 = I. 3: for k= 1,2,...do 4: Ak−1 =: QkRk; /* QR factorization */ 5: Ak:= RkQk; 6: Uk:= Uk−1Qk; /* Update transformation matrix */ 7: end for 8: …

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