Question

Suppose we have a matrix A R. Recall the Golub-Kahan bidiagonalisation pro- cedure and the Lawson-Hanson-Chan (LHC) bidiagonalisation procedure. Answer the folowing questions: (i) Workout the opcration counts required by the Golub-Kahan bidiagonalisation. (ii) Workout the operation counts required by the LHC bidiagonalisation. (iii) Using the rati derive and explain under what circumstances the LHC is com- putationally more advantageous than the Golub-Kahan. (iv) Suppose we have a bidiagonal matrix B e Rn, show that both B B and BB are tridiagonal matrices. Hint: recall that the operation counts of the QR factorisation (using Houscholder reflec- tion) is about 2mn2 -n3. You can relate those two bidiagonalisation procedures to the QR factorisation to work out their operation counts.

Answer 1

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