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We present a new set of algorithms for computation of matrix rational interpolants and one-sided matrix greatest common divisors. Examples of these interpolants include Pad e approximants, Newton-Pad e, Pad e-Hermite, simultaneous Pad e approximants and more generally M-Pad e approximants along with their matrix generalizations. The algorithms are fast and compute all solutions to a given problem. Solutions for all (possibly singular) subproblems along o diagonal paths in a solution table aredoi:10.1137/s0895479897326912 fatcat:jwa6tvzvrjdiva75mor64ryyai