Certified Partial Eigenvalue and Singular Value Computation // Computes the top-k singular triplets or eigenpairs of large sparse and structured matrices: the computation behind principal component analysis on big sparse data, spectral embeddings, and low-rank approximation. Every result carries a numerical certificate with residuals, a backward-error bound, orthogonality loss, and a pass/fail flag, and bounds that can only be estimated are reported as such rather than passed. Centered, scaled, and composed operators are solved through native 'C++' kernels without forming dense matrices. Drop-in replacements for the 'RSpectra' interface are included.