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 "computing the rank profile matrix"):
  Abstract: The row (resp. column) rank profile of a matrix describes the stair case shape of its row (resp. column) echelon form. In an ISSAC'13 paper, we proposed a recursive Gaussian elimination that can compute simultaneously the row and column rank profiles of a matrix, as well as those of all of its leading sub-matrices, in the same time as state of the art Gaussian elimination algorithms. Here we first study the conditions making a Gaussian elimination algorithm reveal this information. We propose the definition of a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank profiles of all the leading sub-matrices. We also explore the conditions for a Gaussian elimination algorithm to compute all or part of this invariant, through the corresponding PLUQ decomposition. As a consequence, we show that the classical iterative CUP decomposition algorithm can actually be adapted to compute the rank profile matrix. Used, in a Crout variant, as a base-case to our ISSAC'13 implementation, it delivers a significant improvement in efficiency. Second, the row (resp. column) echelon form of a matrix are usually computed via different dedicated triangular decompositions. We show here that, from some PLUQ decompositions, it is possible to recover the row and column echelon forms of a matrix and of any of its leading sub-matrices thanks to an elementary post-processing algorithm.

Includes members:
  Member "parallel computation of echelon forms":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "lu factorization with errors")
  Member "simultaneous computation of the row and column rank profiles":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles")
  Member "rank profile revealing gaussian elimination and the cup matrix decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "elimination based certificates for triangular equivalence and rank profiles")
  Member "fast generalized bruhat decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "recursive matrix algorithms in commutative domain for cluster with distributed memory")

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.SC(Symbolic Computation)