We consider weights of the SPOD form
with $\delta(i,j) = 1$ if $i=j$ and 0 else. For the two cases $t=0,1$, we consider the sequences $\beta_{0,j}=\lambda_j$ and $\beta_{1,j}=\lambda_j\pi \max(k_{1,j},k_{2,j})$, where $\lambda_j$ is given by
and where
is an ordering of $\mathbb{N}^2$ such that $k_{1,j}^2+k_{2,j}^2 \le k_{1,j+1}^2+k_{2,j+1}^2$ for all $j\in\mathbb{N}$, and the ordering is arbitrary in the case of equality. Below, we give the generating vectors for $\beta_{t,j}$. These sequences are then $p_t$-summable with $p_0>1/2$, $p_1>2/3$, which, assuming the limiting values, yields the choice $\alpha=2$ for the interlacing factor.
ID | staircase2d_spod |
Generated | 2015-06-25 |
Weight Type | SPOD_2dstaircase |
Publications using these vectors
- Dick, J., Gantner, R.N., Le Gia, Q.T., and Schwab, C. 2015. Higher order Quasi-Monte Carlo integration for Bayesian Estimation. (submitted). (link)
- Dick, J., Kuo, F.Y., Le Gia, Q.T., and Schwab, C. 2014. Multi-level higher order QMC Galerkin discretization for affine parametric operator equations. Report 2014-14 Seminar for Applied Mathematics, ETH Zürich. (link)
Generating Vectors
$\alpha=2$$\boldsymbol{\alpha}$ | $\boldsymbol{C}$ | $\boldsymbol{t}$ | $\boldsymbol{q}$ | Links |
---|---|---|---|---|
2 | 0.1 | 0 | 0 | .tar.gz, .tar.bz2, .zip |
2 | 0.1 | 0 | 1 | .tar.gz, .tar.bz2, .zip |
2 | 0.1 | 0 | 2 | .tar.gz, .tar.bz2, .zip |
2 | 0.1 | 0 | 3 | .tar.gz, .tar.bz2, .zip |
2 | 0.1 | 1 | 0 | .tar.gz, .tar.bz2, .zip |
2 | 0.1 | 1 | 1 | .tar.gz, .tar.bz2, .zip |
2 | 0.1 | 1 | 2 | .tar.gz, .tar.bz2, .zip |
2 | 0.1 | 1 | 3 | .tar.gz, .tar.bz2, .zip |
$\boldsymbol{\alpha}$ | $\boldsymbol{C}$ | $\boldsymbol{t}$ | $\boldsymbol{q}$ | Links |
2 | 0.01 | 0 | 0 | .tar.gz, .tar.bz2, .zip |
2 | 0.01 | 0 | 1 | .tar.gz, .tar.bz2, .zip |
2 | 0.01 | 0 | 2 | .tar.gz, .tar.bz2, .zip |
2 | 0.01 | 0 | 3 | .tar.gz, .tar.bz2, .zip |
2 | 0.01 | 1 | 0 | .tar.gz, .tar.bz2, .zip |
2 | 0.01 | 1 | 1 | .tar.gz, .tar.bz2, .zip |
2 | 0.01 | 1 | 2 | .tar.gz, .tar.bz2, .zip |
2 | 0.01 | 1 | 3 | .tar.gz, .tar.bz2, .zip |