Partial-skew-orthogonal polynomials and related integrable lattices with Pfaffian tau-functions (Q1620832)

A new concept called partial-skew-orthogonal polynomials (PSOPs) is introduced. The authors investigate integrable systems and numerical algorithms associated to (PSOPs) as a modification of the skew-orthogonal polynomials (SOPs). By using appropriate deformations of the weight functions, the authors derive nine integrable lattices in different dimensions. They produce nine integrable systems by considering one (or two)-parameter deformations for PSOPs. Seven integrable lattices including semi (or full)-discrete generalized Toda and Lotka-Voterra lattices of BKP type in different dimensions are derived. Then, the authors produce two discrete integrable lattices. By means of these lattices, they obtain new algorithms to study vector Padé approximants and convergence acceleration of sequence transformations. Also, to compute certain vector Padé approximants, the authors derive a discrete integrable lattice. In the last section, the authors give conclusions and discussions.