We　provide　a　theoretical　study　of　the　iterative　hard　thresholding　with　partially　known　support　set　(IHT-PKS)　algorithm　when　used　to　solve　the　compressed　sensing　recovery　problem.　Recent　work　has　shown　that　IHT-PKS　performs　better　than　the　traditional　IHT　in　reconstructing　sparse　or　compressible　signals.　However,　less　work　has　been　done　on　analyzing　the　performance　guarantees　of　IHT-PKS.　In　this　paper,　we　improve　the　current　RIP-based　bound　of　IHT-PKS　algorithm　from　δ3s−2k＜132≈0.1768　to　δ3s−2k＜5−14,　where　δ3s−2k　is　the　restricted　isometric　constant　of　the　measurement　matrix.　We　also　present　the　conditions　for　stable　reconstruction　using　the　IHTμ-PKS　algorithm　which　is　a　general　form　of　IHT-PKS.　We　further　apply　the　algorithm　on　Least　Squares　Support　Vector　Machines　(LS-SVM),　which　is　one　of　the　most　popular　tools　for　regression　and　classification　learning　but　confronts　the　loss　of　sparsity　problem.　After　the　sparse　representation　of　LS-SVM　is　presented　by　compressed　sensing,　we　exploit　the　support　of　bias　term　in　the　LS-SVM　model　with　the　IHTμ-PKS　algorithm.　Experimental　results　on　classification　problems　show　that　IHTμ-PKS　outperforms　other　approaches　to　computing　the　sparse　LS-SVM　classifier.　©　2023,　Institute　of　Mathematics,　Czech　Academy　of　Sciences.