1. A method for implementing virtual memory in a computer system comprising the steps of: a. maintaining in a memory a table containing entries indicative of the correlation of virtual memory addresses to physical memory addresses; b. maintaining, in a high speed memory, respective translation descriptors relating a variable group of virtual addresses to physical addresses, said descriptors being derivable from said table entries; c. comparing predetermined portions of a virtual address to be translated to said translation descriptors; d. if a matching translation descriptor is found, generating indicia of the physical address by combining a portion of the virtual address with a portion of the matching translation descriptor; and e. if a matching descriptor is not found, generating through a software algorithm a translation descriptor from said table, installing such generated translation descriptor in said high speed memory, then repeating steps c and d.