This paper presents a high-precision Nyström quadrature-discretization method for the coordinate-space Lippmann-Schwinger equation. While the direct application of the Nyström approach is hampered by the derivative jump in the free Green's function, a robust subtraction and smoothing procedure is introduced to regularize this discontinuity. Tested on $p$- and $d$-wave scattering for two model potentials, this regularization is shown to be essential for numerical stability, yielding 8-digit accuracy for the partial-wave $S$ matrices with a relatively small set of quadrature points. Because full Nyström matrices can become computationally prohibitive for large-scale applications, there exists a need for contracting this high-fidelity information into a more compact representation. Petrov-Galerkin approaches appear appropriate for this purpose. Among many possibilities, the Bateman approximation, Schwinger variational method and Newton variational method appear especially promising. Bateman method for the resolvent is of interest because an interesting connection exists between Nyström and Bateman methods. Numerical results confirm that the Bateman procedure successfully reduces the information content of large-scale Nyström calculations into a compact form with reasonable accuracy, while the Schwinger and Newton variational methods exhibit even higher efficiency in this reduction task. This compression of high-fidelity Nyström information into a minimal basis resembles the data-contraction techniques prevalent in modern machine learning and emulation.

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• Few-body systems
• Scattering theory