human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "symmetric indefinite triangular factorization revealing the rank profile matrix"):
  Abstract: We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} = \mathbf{L}\mathbf{D}\mathbf{L}^T$ where $\mathbf{P}$ is a permutation matrix, $\mathbf{L}$ is lower triangular with a unit diagonal and $\mathbf{D}$ is symmetric block diagonal with $1{\times}1$ and $2{\times}2$ antidiagonal blocks. The novel algorithm requires $O(n^2r^{\omega-2})$ arithmetic operations. Furthermore, experimental results demonstrate that our algorithm can even be slightly more than twice as fast as the state of the art unsymmetric Gaussian elimination in most cases, that is it achieves approximately the same computational speed. By adapting the pivoting strategy developed in the unsymmetric case, we show how to recover the rank profile matrix from the permutation matrix and the support of the block-diagonal matrix. There is an obstruction in characteristic $2$ for revealing the rank profile matrix which requires to relax the shape of the block diagonal by allowing the 2-dimensional blocks to have a non-zero bottom-right coefficient. This relaxed decomposition can then be transformed into a standard $\mathbf{P}\mathbf{L}\mathbf{D}\mathbf{L}^T\mathbf{P}^T$ decomposition at a negligible cost.

Includes members:
  Member "fast computation of the rank profile matrix and the generalized bruhat decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles")
  Member "computing the rank profile matrix":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on the uniqueness of simultaneous rational function reconstruction")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.NA(Numerical Analysis)