An essential primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one smaller bond dimension. This forms central bottleneck algorithms for time evolution and contracting projected entangled pair states. We formulate tangent-space based variational algorithm to achieve this goal uniform (infinite) The exhibits favourable scaling computationa...

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...