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23 Oct 2014: k arethe node points and the quadrature weights of a quadrature formula, respectively.Here r is an integer with the requirement: 2 r k. ... b. gd(xN ) cos. ( πxNb. ))T,. (39). where U (t) denotes the N -dimensional vector with entries ui(t) u(xi, t),.

5 May 2015: In the context of the Schrödinger equation (1.1), this represented asignificant improvement over the more stringent convergence requirements of (Iserles& Nørsett 1999, Moan & Niesen 2008) which were obtained under a

26 Sep 2005: Acta Numerica (2005), pp. 1–148 c Cambridge University Press, 1999. Lie-group methods. Arieh Iserles. Department of Applied Mathematics and Theoretical Physics,. University of Cambridge, England. Email: a.iserles@damtp.cam.ac.uk. Hans Z.

27 Aug 2014: The requirement dT Qk(p) < 0 before α iscalculated provides α > 0.

5 Oct 2013: Yet, as we shall now see, by dropping the requirement of consistency, we obtain areconstruction which circumvents the aforementioned issues associated with (3.2). ... This requirement is quite strong as we may verywell have that W /= H and S = H (e.g.

2 Nov 2016: In Figure 4 we plot the absolute values of the entries of the matrix U for these threeexamples. ... r} {1,. ,r} be a permutation and let V be the matrix with entries vkl =δl,π(k).

24 Oct 2016: Analyzing the structure of multidimensional compressedsensing problems through coherence. A. JonesUniversity of Cambridge. B. AdcockSimon Fraser Univesity. A. HansenUniversity of Cambridge. Abstract. Recently it has been established that asymptotic

24 Jul 2018: wavelets) called sparsitybasis. This means that its vector of coefficients x = Φf has at mosts nonzero entries. ... Fig. 5 shows theabsolute values of the entries of the matrix U for three examples.

10 Jun 2014: Analyzing the Structure of Multidimensional CompressedSensing Problems through Coherence. A. JonesUniversity of Cambridge. B. AdcockPurdue Univesity. A. HansenUniversity of Cambridge. Abstract. In previous work it was established that asymptotic

14 Sep 2005: , f =. . f(x0). f(m01)(x0) f(xν). f(mν1)(xν). . For notational brevity we regard matrices as row vectors whose entries are column

6 Dec 2020: In other words, one can introduce zeros in the column below the diagonal entry. ... many non-zero entries in each column then we can replace WOT convergence by SOT convergence.

26 Mar 2014: l = 1,2,., (5). where π is a bijection that gives a nonincreasing rearrangement of the entries ofc(l), i.e. ... row (as opposed to row block) to be the maximum of its entries in that row.

21 Oct 2014: The division into only eight levels is both to minimise the additional storage requirements for this information, and in the realisation that a greater degree of precision in determining the true ... While this may produce some mismatching, the

14 Jun 2017: range. It is then in the next subsection, in Theorems 8–10, that this fine and coarsedecomposition is shown to bear fruit in the form of reduced requirements for quadrature. ... + sin. (ωλ ,1(ck,ck1)t. )t. [gλ ,1(ck,ck hkt)]3,100. .

24 Oct 2016: Analyzing the structure of multidimensional compressedsensing problems through coherence. A. JonesUniversity of Cambridge. B. AdcockSimon Fraser Univesity. A. HansenUniversity of Cambridge. Abstract. Recently it has been established that asymptotic

22 Nov 2011: Because of the stringent requirements placed on thereconstruction basis, spectral reprojection consequently affords little flexibility to the user. ... Then En,m =‖B‖, where B Cnn is the Hermitian matrix. with (j,k)th entry 〈φj Pmφj,φk Pmφk〉R.

5 Oct 2013: Because of the stringent requirements placed on thereconstruction basis, spectral reprojection consequently affords little flexibility to the user. ... Then En,m =‖B‖, where B Cnn is the Hermitian matrix. with (j, k)th entry 〈φj Pmφj , φk

21 Jan 2016: the || nonzero entries are allowed tohave arbitrary locations in N, regardless of the reconstruction algorithm used [15]. ... In particular, condition (5.7) is the requirementon the magnitude of the off-diagonal entries of the matrix PMUPNUPM.

2 Nov 2016: In Figure 4 we plot the absolute values of the entries of the matrix U for these threeexamples. ... r} {1,. ,r} be a permutation and let V be the matrix with entries vkl =δl,π(k).