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4 Mar 2005: t3). (5.16). Thus,etBetC = et(BC) t 0 only if B andC commute.[Note: It is trivial to prove that commutativityis sufficient, not just necessary.]The good news is, however,

21 Feb 2005: to the grid) pass unnoticed!Bad news:For |θ|, |ψ| = O. (. ... small attenuation already familiar from the analysis of Gauss–Seidel.Good news:Consider just thelarge frequencies.Then.

7 Feb 2005: . . You should find that the(2, 3) element of the new matrix isO(. ... ε3). and that the new matrix has exactly thesame trace asA.

7 Feb 2005: Definition 3.10 (Multistep methods)It is often useful to use past solution values in computing a new value.Thus, assuming thatyn, yn1,. ,

31 Jan 2005: adjacent columns of a matrix, thetotal number of nonzero elements in the new combination of rows or columns is at most five.

19 Jan 2005: It follows from the symmetry ofAand the new assertion(2) that the proof is complete.

25 Jan 2005: The reason for the new step2 is thatf (λ) = 0 implies thatx(k) satisfiesAx(k) = (λ s(k))x(k).

15 Aug 2005: conveniently modified version of the Magnus expansion to construct a new class of. ... Here new Lie group solvers up to order four for (2) are presented.

14 Sep 2005: ωs1. ). Like the Filon-type method, this new method uses interior points as. ... A[. ddx. fg′. ]. Hence we have derived a new approximation of I[f], namely QA[f] 1iωQ.

23 Nov 2005: Even then the singularity of h. (with the new definition of f̃) at ξ is not removable.

21 Sep 2005: This results in a new system,. di. dxiL[v](ck) =. di. dxif(ck), i = 1, 2,. ... W. J. (1974), Asymptotics and Special Functions, Academic Press, New. York.Olver, S.

29 Jan 2005: We now remove the bottom row of R and denote the new matrix by R̃. ... S. (1994), Introduction to Mechanics and Symmetry,Springer-Verlag, New York. Olver, P.

24 Feb 2005: Proposition 11 is of particular importance for our purpose andseems to be new. ... Springer–Verlag, 1989. [11] K. Scherer and A. Shadrin. New upper bound for the B-spline basis conditionnumber.

3 Oct 2005: Academic Press, New York, NY. Olver, S. (2005). Moment-free numerical integration of highly oscillatory functions. ... Rudin, W. (1964). Principles of Mathematical Analysis. McGraw-Hill, Inc., New York, NY.

14 Dec 2005: Therefore, in order to get closer to the value 2k 1, it is necessary to proposea new approach. ... Jacobi projections in: Approximation theory and applications (ZviZiegler, ed.), Academic Press, New York, 1981, 187–200.

17 Feb 2005: Quadrature methods for multivariate highly. oscillatory integrals using derivatives. Arieh Iserles and Syvert P. Nørsett†. We dedicate this paper to the memory of Germund Dahlquist. Abstract. While there exist effective methods for univariate

26 Sep 2005: A familiar case in pointis the discovery of solitons in the solution of the Korteweg–de Vries equation byZabusky and Kruskal (1965), an event which launched a whole new mathematicaldiscipline, other