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 "certified roundoff error bounds using bernstein expansions and sparse krivine stengle representations"):
  Abstract: Floating point error is a drawback of embedded systems implementation that is difficult to avoid. Computing rigorous upper bounds of roundoff errors is absolutely necessary for the validation of critical software. This problem of computing rigorous upper bounds is even more challenging when addressing non-linear programs. In this paper, we propose and compare two new algorithms based on Bernstein expansions and sparse Krivine-Stengle representations, adapted from the field of the global optimization, to compute upper bounds of roundoff errors for programs implementing polynomial and rational functions. We also provide the convergence rate of these two algorithms. We release two related software package FPBern and FPKriSten, and compare them with the state-of-the-art tools. We show that these two methods achieve competitive performance, while providing accurate upper bounds by comparison with the other tools.

Includes members:
  Member "certified roundoff error bounds using semidefinite programming":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "exact optimization via sums of nonnegative circuits and sums of am gm exponentials")
  Member "towards a compiler for reals":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "automatic generation and verification of test stable floating point code")
  Member "formal verification of nonlinear inequalities with taylor interval approximations":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "deciding univariate polynomial problems using untrusted certificates in isabelle hol")
  Member "certification of bounds on expressions involving rounded operators":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "abstract compilation for verification of numerical accuracy properties")
  Member "introduction to the ginac framework for symbolic computation within the c programming language":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the fly optimization of parallel computation of symbolic symplectic invariants")

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)