Summary: We present new large-update primal-dual interior point algorithms for \(P_* \) linear complementarity problems(LAPS) based on a class of kernel functions, \( \psi(t)= \frac{t^{p+1}-1}{p+1}+\frac {1}{\sigma}(e^{\sigma(1-t)}-1), p\in[0,1],\sigma\geq 1\). It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for \(P_* \) LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for \(P_* \) LAPS have \(O((1+2\kappa)n^{\frac{1}{p+1}}\log{n} \log\frac{n}{\varepsilon})\) complexity bound. When \(p=1\), we have \( O((1+2\kappa)\sqrt{n}\log {n}\log\frac{n}{\varepsilon})\) complexity which is so far the best known complexity for large-update methods.