In this paper we propose new large-update primal-dual interior point algorithms for $P_{ eq}({kappa})$ linear complementarity problems(LCPs). New search directions and proximity measures are proposed based on a specific class of kernel functions, ${psi}(t)={frac{t^{p+1}-1}{p+1}}+{frac{t^{-q}-1}{q}}$, q>0, $p{in}[0,;1]$, which are the generalized form of the ones in [3] and [12]. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*({kappa})$LCPs. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*({kappa})$ LCPs have the best known complexity $O((1+2{kappa}){sqrt{2n}}(log2n)log{frac{n}{varepsilon}})$ when p=1 and $q=frac{1}{2}(log2n)-1$.