We describe improved algorithms for carrying out pseudospectral Hartree-Fock calculations; these algorithms are applicable to other ab initio electronic structure methodologies as well. Absolute energies agree with conventional basis set codes to within 0.25 kcal/mol, and relative energies agree to better than 0.1 kcal/mol for a wide variety of test molecules. Accelerations of CPU times of as large as a factor of 6.5 are obtained as compared to GAUSSIAN 92, with the actual timing advantage increasing for larger basis sets and larger molecules. The method is shown to be highly reliable and capable of handling extended basis sets.