  We present a method for accurate determination of atomic transition matrix
elements at the 10^{-3} level. Measurements of the ac Stark (light) shift
around "magic-zero" wavelengths, where the light shift vanishes, provide
precise constraints on the matrix elements. We make the first measurement of
the 5s-6p matrix elements in rubidium by measuring the light shift around the
421 nm and 423 nm zeros with a sequence of standing wave pulses. In conjunction
with existing theoretical and experimental data, we find 0.3236(9) e a_0 and
0.5230(8) e a_0 for the 5s-6p_{1/2} and 5s-6p_{3/2} elements, respectively, an
order of magnitude more accurate than the best theoretical values. This
technique can provide needed, accurate matrix elements for many atoms,
including those used in atomic clocks, tests of fundamental symmetries, and
quantum information.
