How do I code normalized global errors in Matlab?

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Kayode Odeyemi 2020-6-29

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https://ww2.mathworks.cn/matlabcentral/answers/556585-how-do-i-code-normalized-global-errors-in-matlab

编辑： Kayode Odeyemi 2020-6-29

If I is defined to be a discrete approximation to the global integral then

I(h)=\frac{1}{4\pi} \int_{0}^{2\pi}\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}h(\lambda,\theta)\cos{\theta} {d\theta} d\lambda
I need help on how to write a Matlab code for the following normalized global errors:
l_{1}(h)=\frac{I[|h(\lambda, \theta)-h_{T}(\lambda, \theta)|]}{I[|h_{T}(\lambda, \theta)|]}
l_{2}(h)=\frac{\{I[(h(\lambda, \theta)-h_{T}(\lambda, \theta))^2]\}^{1/2}}{\{I[h_{T}(\lambda, \theta)^2]\}^{1/2}}
l_{\infin}(h)=\frac{\max_{all\lambda,\theta}|h(\lambda, \theta)-h_{T}(\lambda, \theta)|}{\max_{all\lambda,\theta}|h_{T}(\lambda, \theta)|}
where h_{T} is the true solution.