Rump, Siegfried M.Siegfried M.Rump2026-10-012026-10-012026-09-18Japan Journal of Industrial and Applied Mathematics 43: 61 (2026)https://hdl.handle.net/11420/65131The Matlab/Octave toolbox INTLAB offers many so-called verification algorithms the results of which are correct with mathematical certainty. Starting in 1998 INTLAB is continuously enhanced. The latest Version 14.1 comprises 2083 m-files with more than 76,000 lines of code (with comments more than 137,000). There are several thousand users in more than 50 countries. We describe fundamentals and latest developments in INTLAB including fast and accurate real and complex, full and sparse matrix residuals, sparse linear, in particular nearly symmetric as well as nonlinear systems, and matrix decompositions. Several executable Matlab/Octave codes are included throughout the sections.en1868-937X2026SpringerFull and sparse linear and nonlinear systemsINTLABMathematically rigorous error boundsNumerical analysisOptimizationReliable computingNatural Sciences and Mathematics::510: MathematicsJournal Article10.1007/s13160-026-00814-w