human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "certified roundoff error bounds using semidefinite programming"
  Abstract: Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs or custom hardware implementations. This problem becomes challenging when the program does not employ solely linear operations, and non-linearities are inherent to many interesting computational problems in real-world applications. #R##N#Existing solutions to reasoning possibly lead to either inaccurate bounds or high analysis time in the presence of nonlinear correlations between variables. Furthermore, while it is easy to implement a straightforward method such as interval arithmetic, sophisticated techniques are less straightforward to implement in a formal setting. Thus there is a need for methods which output certificates that can be formally validated inside a proof assistant. #R##N#We present a framework to provide upper bounds on absolute roundoff errors of floating-point nonlinear programs. This framework is based on optimization techniques employing semidefinite programming and sums of squares certificates, which can be checked inside the Coq theorem prover to provide formal roundoff error bounds for polynomial programs. Our tool covers a wide range of nonlinear programs, including polynomials and transcendental operations as well as conditional statements. We illustrate the efficiency and precision of this tool on non-trivial programs coming from biology, optimization and space control. Our tool produces more accurate error bounds for 23% of all programs and yields better performance in 66% of all programs.

Connected through hyperedge HE-1 (induced by source paper "exact optimization via sums of nonnegative circuits and sums of am gm exponentials"):
  with members:
    - "on exact polya hilbert artin and putinar s representations"
    - "on exact polya and putinar s representations"
    - "realcertify a maple package for certifying non negativity"
    - "formal proofs for nonlinear optimization"

Connected through hyperedge HE-2 (induced by source paper "certified roundoff error bounds using bernstein expansions and sparse krivine stengle representations"):
  with members:
    - "towards a compiler for reals"
    - "formal verification of nonlinear inequalities with taylor interval approximations"
    - "certification of bounds on expressions involving rounded operators"
    - "introduction to the ginac framework for symbolic computation within the c programming language"

Connected through hyperedge HE-3 (induced by source paper "sound approximation of programs with elementary functions"):
  with members:
    - "sound mixed precision optimization with rewriting"
    - "towards a compiler for reals"
    - "robustness analysis of finite precision implementations"

Connected through hyperedge HE-4 (induced by source paper "a verified certificate checker for finite precision error bounds in coq and hol4"):
  with members:
    - "on sound relative error bounds for floating point arithmetic"
    - "a linear first order functional intermediate language for verified compilers"
    - "towards a compiler for reals"
    - "formal verification of nonlinear inequalities with taylor interval approximations"
    - "robustness analysis of finite precision implementations"
    - "wave equation numerical resolution a comprehensive mechanized proof of a c program"
    - "certification of bounds on expressions involving rounded operators"
    - "a static analyzer for large safety critical software"

Connected through hyperedge HE-5 (induced by source paper "sound mixed precision optimization with rewriting"):
  with members:
    - "on sound relative error bounds for floating point arithmetic"
    - "towards a compiler for reals"
    - "robustness analysis of finite precision implementations"
    - "wave equation numerical resolution a comprehensive mechanized proof of a c program"
    - "synthesis of minimal error control software"
    - "a static analyzer for large safety critical software"

Connected through hyperedge HE-6 (induced by source paper "on sound relative error bounds for floating point arithmetic"):
  with members:
    - "on the maximum relative error when computing x n in floating point arithmetic"
    - "towards a compiler for reals"
    - "wave equation numerical resolution a comprehensive mechanized proof of a c program"
    - "certification of bounds on expressions involving rounded operators"

Connected through hyperedge HE-7 (induced by source paper "interval enclosures of upper bounds of roundoff errors using semidefinite programming"):
  with members:
    - "certified roundoff error bounds using bernstein expansions and sparse krivine stengle representations"
    - "certification of bounds on expressions involving rounded operators"

Question: Please tell me which class the center node 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)