Potentialities of Hubble parameter and expansion rate function data to alleviate Hubble tension

Taking advantage of Gaussian process (GP), we obtain an improved estimate the Hubble constant, $H_0=70.41\pm1.58$ km s$^{-1}$ Mpc$^{-1}$, using parameter [$H(z)$] from cosmic chronometers (CCH) and expansion rate function [$E(z)$], extracted type Ia supernovae, data. We also use CCH data, including ones with full covariance matrix, $E(z)$ data to a determination $H_0=72.34_{-1.92}^{+1.90}$ which implies that involvement matrix results in higher values uncertainties $H_0$. These are than those obtained by directly reconstructing GP. In order potential future simulate two sets $H(z)$ them constrain $H_0$ either GP reconstruction or fitting find simulated alleviate tension pushing towards $\sim70$ Mpc$^{-1}$. joint + favor $H_0$, is confirmed constraining flat concordance model 2-order Taylor $H(z)$. summary, conclude more better-quality as well can provide new useful perspective on resolving tension.