We consider the allocation of spectral and power resources every subframe (1 ms) on the uplink of the Long Term Evolution (LTE) wideband orthogonal frequency division multiple access (OFDMA) cellular network. System bandwidth is divided into multiple sub-bands. The fractional power control to manage interference is allowed to be sub-band dependent. Moreover, the channel gains from the base-station to the mobiles (user equipment (UE) in LTE) can vary with the sub-band. The power and spectral resources are to be allocated among different UEs in a cell based on channel conditions, desired fairness/QoS, and constraints on power due to interference and power limitation at a UE. For N UEs and M sub-bands, we exploit the structure of the underlying optimization problem to obtain an interior point method for optimal resource allocation where each Newton step has complexity O(NM). To implement this in an OFDMA system, we delineate a simple control signalling structure where the UE computes in O(M) time a waterfllling solution every subframe it is assigned resources. When the allocation is restricted to contiguous allocation in frequency due to single carrier constraint in LTE, we convert the solution computed above into a feasible solution in O(NM) time. For typical network scenarios, the solution thus computed is numerically shown to be very close to the optimal solution without the contiguous constraint.