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We describe a new multifractal finite-size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simulations of system sizes up to L^3 = 120^3 and involving nearly 10^6 independent wave functions have yielded unprecedented precision for the critical disorder Wc = 16.530(16.524,16.536) and the critical exponent v = 1.590(1.579,1.602). We find that the multifractal exponents Delta_q exhibit a previously predicted symmetry relation and we confirm the nonparabolic nature of their spectrum. We present in detail the MFSS procedure first introduced in our Letter [Phys. Rev. Lett. 105, 046403 (2010)]. The MFSS procedure is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point. |