RANDOMIZED NUMERICAL LINEAR ALGEBRA FOR THE COMPUTATIONAL DETECTION OF FAILURES IN THE EXTERNAL EVALUATION OF ANGOLA'S HIGHER EDUCATION INSTITUTIONS: SELF-AUTHORED PYTHON ALGORITHMS AND AN ORIGINAL EXPERIMENTAL METHOD IN SUPPORT OF INAAREES

Resumen

Africa's educational challenge has shifted from quantity to an acute crisis of quality. In Angola, the National Institute for Assessment, Accreditation and Recognition of Higher Education Studies (INAAREES)[1] carried out, between 2023 and 2026, five external evaluation rounds covering 671 study programmes, of which 253 (37.7%) failed accreditation  empirical evidence of the subsystem's quality deficit. However, the growing volume of indicators collected in each evaluation cycle makes purely manual analysis slow, costly and error-prone. This paper proposes, for the first time in Angola, the application of randomized numerical linear algebra (RandNLA)[2] to the computational detection of failures in higher education external evaluations. We introduce an original matrix model of external evaluation (programmes × indicators), four self-authored Python algorithms  SRVD, RSDF, DICA-R and a Failure Risk Index (IRF)  and a self-designed experimental method using a synthetic 671 × 14 matrix calibrated with official INAAREES aggregates, with 60 a priori known injected failures. Results show that SRVD matches the Eckart-Young optimum (maximum deviation of 0.003 percentage points) with speedups up to 37.9× on large matrices; the hybrid RSDF+DICA-R detector recovered 60/60 failures at the top-60 cut-off (100% precision; AUC-PR = 0.976); and the IRF correlates at r = 0.633 with the true institutional failure rate. A dedicated analysis of engineering programmes  the field assessed in the STEM (4th) phase  evidences the robust strand of the national quality assurance framework. Randomization thus provides a viable, scalable and auditable triage instrument for external evaluation committees.