Computational benefit of smoothness: parameterized bit-complexity of numerical operators on analytic functions and Gevrey's hierarchy
From MaRDI portal
Publication:491087
DOI10.1016/j.jco.2015.05.001zbMath1336.68133OpenAlexW235490522MaRDI QIDQ491087
Akitoshi Kawamura, Carsten Rösnick, Martin Ziegler, Norbert Th. Müller
Publication date: 24 August 2015
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jco.2015.05.001
Analysis of algorithms and problem complexity (68Q25) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Complexity and performance of numerical algorithms (65Y20) Computation over the reals, computable analysis (03D78)
Related Items (7)
Exact real computation of solution operators for linear analytic systems of partial differential equations ⋮ Comparing representations for function spaces in computable analysis ⋮ Towards Computational Complexity Theory on Advanced Function Spaces in Analysis ⋮ Bit-complexity of classical solutions of linear evolutionary systems of partial differential equations ⋮ Representations of Analytic Functions and Weihrauch Degrees ⋮ Parametrised second-order complexity theory with applications to the study of interval computation ⋮ Representations and evaluation strategies for feasibly approximable functions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Real computation with least discrete advice: a complexity theory of nonuniform computability with applications to effective linear algebra
- Lipschitz continuous ordinary differential equations are polynomial-space complete
- Representation theorems for analytic machines and computability of analytic functions
- On the computational complexity of the Riemann mapping
- The computational complexity of maximization and integration
- The maximum value problem and NP real numbers
- Computational complexity of real functions
- Some new characterizations of the Chebyshev polynomials
- A fundamental effect in computations on real numbers
- Computability on subsets of Euclidean space. I: Closed and compact subsets
- An effective Riemann Mapping Theorem
- Why does information-based complexity use the real number model?
- Computational complexity and feasibility of data processing and interval computations
- Rational presented metric spaces and complexity, the case of the space of real functions uniformly continuous on a compact interval
- Topological properties of real number representations.
- Effective analytic functions
- On effective analytic continuation
- Parametrized complexity theory.
- Analytical properties of resource-bounded real functionals
- The Arithmetical Hierarchy of Real Numbers
- Condition
- Algorithmic solution of higher type equations
- Computational Complexity of Smooth Differential Equations
- Computing Conformal Maps onto Canonical Slit Domains
- Relative computability and uniform continuity of relations
- The Exponentially Convergent Trapezoidal Rule
- Low functions of reals
- Solving Analytic Differential Equations in Polynomial Time over Unbounded Domains
- Computable operators on regular sets
- Spaces allowing Type‐2 Complexity Theory revisited
- On the definitions of computable real continuous functions
- On the computational complexity of ordinary differential equations
- Singular coverings and non‐uniform notions of closed set computability
- A critique of numerical analysis
- Resultats d'unicite forte pour des operateurs elliptiques a coefficients gevrey
- On a simple definition of computable function of a real variable‐with applications to functions of a complex variable
- Computability on Regular Subsets of Euclidean Space
- Computational complexity on computable metric spaces
- Lower Bounds on the Continuation of Holomorphic Functions
- Function Spaces for Second-Order Polynomial Time
- Analytic Root Clustering: A Complete Algorithm Using Soft Zero Tests
- On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction
- ROUNDING-OFF ERRORS IN MATRIX PROCESSES
- Algorithms in real algebraic geometry
This page was built for publication: Computational benefit of smoothness: parameterized bit-complexity of numerical operators on analytic functions and Gevrey's hierarchy
