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6 Dec 2020: The SCI provides a classificationhierarchy [8,9,24–27,42] of spectral problems according to their computational difficulty.

23 Nov 2020: Time, location: Online. This is a Part II course in numerical analysis given in Michaelmas term 2020 that contains 24 lectures. ... Lecture 16:Lecture 17:Lecture 18:Week 7:. Lecture 19:Lecture 20:Lecture 21:Week 8:. Lecture 22:Lecture 23:Lecture

6 Oct 2020: 24. The QR algorithm. Convergence of the first column and the bottom row.

26 Oct 2020: etBetC = et(BC) 12t2(BC CB) O(t3). (2.24). In particular, etBetC = et(BC) for all t 0 if and only if B and C commute.

26 Oct 2020: 24. the even and odd portions of y, respectively. Note that y(E),y(O) Πm.

29 Oct 2020: 19 on the Example Sheets). Method 3.24 (The spectral method for evolutionary PDEs) We consider the problemu(x,t). ... û′n(t) = π2n2ûn(t). n ΓN (3.24). Its exact solution is ûn(t) = eπ2n2t ĝn for n 6= 0 and we set û0(t) = 0 due to

16 Nov 2020: This gives expression for αk in (4.7). 37. Method 4.24 (The steepest descent method) This method takes d(k) =F1(x(k)) = b Ax(k)for every k, the

21 Oct 2020: 24 / 28. Splitting of inhomogeneous systems. Recall our goal, namely fast methods for the two-dimensionaldiffusion equation.

26 Oct 2020: N/2. (12). 24 / 27. Computation of Fourier coefficients (DFT).

28 Oct 2020: 24 / 29. Analyticity and periodicity – Relaxing periodicity. Relaxing periodicity: Disappointingly, periodicity is necessary forspectral convergence.