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 "stability of the lanczos method for matrix function approximation"):
  Abstract: The ubiquitous Lanczos method can approximate $f(A)x$ for any symmetric $n \times n$ matrix $A$, vector $x$, and function $f$. In exact arithmetic, the method's error after $k$ iterations is bounded by the error of the best degree-$k$ polynomial uniformly approximating $f(x)$ on the range $[\lambda_{min}(A), \lambda_{max}(A)]$. However, despite decades of work, it has been unclear if this powerful guarantee holds in finite precision. #R##N#We resolve this problem, proving that when $\max_{x \in [\lambda_{min}, \lambda_{max}]}|f(x)| \le C$, Lanczos essentially matches the exact arithmetic guarantee if computations use roughly $\log(nC\|A\|)$ bits of precision. Our proof extends work of Druskin and Knizhnerman [DK91], leveraging the stability of the classic Chebyshev recurrence to bound the stability of any polynomial approximating $f(x)$. #R##N#We also study the special case of $f(A) = A^{-1}$, where stronger guarantees hold. In exact arithmetic Lanczos performs as well as the best polynomial approximating $1/x$ at each of $A$'s eigenvalues, rather than on the full eigenvalue range. In seminal work, Greenbaum gives an approach to extending this bound to finite precision: she proves that finite precision Lanczos and the related CG method match any polynomial approximating $1/x$ in a tiny range around each eigenvalue [Gre89]. #R##N#For $A^{-1}$, this bound appears stronger than ours. However, we exhibit matrices with condition number $\kappa$ where exact arithmetic Lanczos converges in $polylog(\kappa)$ iterations, but Greenbaum's bound predicts $\Omega(\kappa^{1/5})$ iterations. It thus cannot offer significant improvement over the $O(\kappa^{1/2})$ bound achievable via our result. Our analysis raises the question of if convergence in less than $poly(\kappa)$ iterations can be expected in finite precision, even for matrices with clustered, skewed, or otherwise favorable eigenvalue distributions.

Includes members:
  Member "spectrum approximation beyond fast matrix multiplication algorithms and hardness":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "schatten norms in matrix streams hello sparsity goodbye dimension")
  Member "lazysvd even faster svd decomposition yet without agonizing pain":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "backward feature correction how deep learning performs deep learning")
  Member "faster algorithms for computing the stationary distribution simulating random walks and more":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "spectral sparsification via bounded independence sampling")
  Member "principal component projection without principal component analysis":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "over parameterized adversarial training an analysis overcoming the curse of dimensionality")
  Member "randomized block krylov methods for stronger and faster approximate singular value decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "homogeneous network embedding for massive graphs via reweighted personalized pagerank")
  Member "large scale log determinant computation through stochastic chebyshev expansions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "schatten norms in matrix streams hello sparsity goodbye dimension")
  Member "the noisy power method a meta algorithm with applications":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "distributed stochastic algorithms for high rate streaming principal component analysis")
  Member "approximating the exponential the lanczos method and an tilde o m time spectral algorithm for balanced separator":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "a deterministic algorithm for balanced cut with applications to dynamic connectivity flows and beyond")

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.DS(Data Structures and Algorithms)