The objectives of this research are (A) highly accurate calculations on small systems for comparison with recent high precision measurements, and (B) the development of better computational methods, where "better" means greater accuracy and reliability with a smaller expenditure of computer time. Specific problems to be considered include (1) The 1/Z expansion, (2) Bethe logarithms and other matrix elements of functions of operators, (3) Hydrogen in strong magnetic fields, (4) Basis functions for problems with multiple length scales, (5) High precision calculations for lithium atoms, (6) Simplification of the Fock expansions, and (7) A priori estimates of non-linear parameters in basis functions.
