Journal of Complexity, ISSN 0885-064X, 12/2019, Volume 55, p. 101425

We study EC-(s,t)-weak tractability of multivariate linear problems in the average case setting. This paper extends earlier work in the worst case setting. The...

Linear problem | Hilbert space | Linear tensor product problem | Average case setting | EC-[formula omitted]-weak tractability | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | APPROXIMATION | INTEGRATION | EC-(s, t)-weak tractability | SPACES

Linear problem | Hilbert space | Linear tensor product problem | Average case setting | EC-[formula omitted]-weak tractability | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | APPROXIMATION | INTEGRATION | EC-(s, t)-weak tractability | SPACES

Journal Article

Journal of Complexity, ISSN 0885-064X, 12/2017, Volume 43, pp. 76 - 102

Many authors have studied exponentially-convergent tractability (EC-tractability) in the worst case setting. Here, we study EC-tractability in the average case...

Tractability | Korobov kernel | Linear problem | Eigenvalue | Average case setting | EC-tractability | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | INTEGRATION

Tractability | Korobov kernel | Linear problem | Eigenvalue | Average case setting | EC-tractability | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | INTEGRATION

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 03/2019, Volume 239, pp. 51 - 71

We consider d-variate approximation problems in the average case setting in the weighted L2 space with the standard Gaussian weight. This space is equipped...

Tractability | Gaussian covariance kernels | Average case setting | Exponential convergence tractability | MATHEMATICS | EXPONENTIAL CONVERGENCE | T)-WEAK TRACTABILITY | Algorithms

Tractability | Gaussian covariance kernels | Average case setting | Exponential convergence tractability | MATHEMATICS | EXPONENTIAL CONVERGENCE | T)-WEAK TRACTABILITY | Algorithms

Journal Article

Journal of Complexity, ISSN 0885-064X, 04/2019, Volume 51, pp. 110 - 128

We study linear multivariate problems defined as the approximation of compact linear multivariate operators over Hilbert spaces. We provide necessary and...

Tractability | Linear multivariate problems | Approximation of operators | Exponential tractability | Complexity | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | INTEGRATION | SPACES | CONVERGENCE

Tractability | Linear multivariate problems | Approximation of operators | Exponential tractability | Complexity | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | INTEGRATION | SPACES | CONVERGENCE

Journal Article

Journal of Complexity, ISSN 0885-064X, 12/2019, Volume 55, p. 101412

This paper is devoted to discussing multivariate approximation problems with analytic Korobov kernels in the worst and average case settings. We consider...

Analytic Korobov kernels | Exponential convergence tractability | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | INTEGRATION | NUMBERS | LINEAR-PROBLEMS | AVERAGE-CASE TRACTABILITY | ENTROPY

Analytic Korobov kernels | Exponential convergence tractability | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | INTEGRATION | NUMBERS | LINEAR-PROBLEMS | AVERAGE-CASE TRACTABILITY | ENTROPY

Journal Article

Journal of Complexity, ISSN 0885-064X, 12/2019, Volume 55, p. 101411

Many authors have studied exponentially-convergent tractability in the worst case setting. But almost all articles related to tractability are focused on the...

Tractability | Eigenvalue | Worst case setting | Product of simplices | Multivariate approximation | EC-tractability | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | WEAK TRACTABILITY | MULTIVARIATE INTEGRATION

Tractability | Eigenvalue | Worst case setting | Product of simplices | Multivariate approximation | EC-tractability | MATHEMATICS | MATHEMATICS, APPLIED | EXPONENTIAL CONVERGENCE | WEAK TRACTABILITY | MULTIVARIATE INTEGRATION

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 08/2017, Volume 145, Issue 8, pp. 3297 - 3310

We study high-dimensional numerical integration in the worst-case setting. The subject of tractability is concerned with the dependence of the worst-case...

Tractability | Pseudorandom numbers | Quasi-Monte Carlo | Weighted star discrepancy | DIMENSIONALITY | MATHEMATICS | EXPONENTIAL-SUMS | MATHEMATICS, APPLIED | pseudorandom numbers | quasi-Monte Carlo | NUMERICAL-INTEGRATION | CURSE | tractability

Tractability | Pseudorandom numbers | Quasi-Monte Carlo | Weighted star discrepancy | DIMENSIONALITY | MATHEMATICS | EXPONENTIAL-SUMS | MATHEMATICS, APPLIED | pseudorandom numbers | quasi-Monte Carlo | NUMERICAL-INTEGRATION | CURSE | tractability

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 07/2016, Volume 207, pp. 301 - 338

We study multivariate approximation defined over tensor product Hilbert spaces. The space is a weighted tensor product Hilbert space with exponential weights...

Tractability | Multivariate approximation | Hilbert spaces with exponential weights | KOROBOV SPACES | MATHEMATICS | INTEGRATION

Tractability | Multivariate approximation | Hilbert spaces with exponential weights | KOROBOV SPACES | MATHEMATICS | INTEGRATION

Journal Article

Journal of Complexity, ISSN 0885-064X, 08/2015, Volume 31, Issue 4, pp. 617 - 636

We study d-variate general linear problems defined over Hilbert spaces in the average case setting. We consider algorithms that use finitely many evaluations...

Linear problem | Eigenvalue | Exponential convergence-tractability | Average case setting | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | MULTIVARIATE INTEGRATION

Linear problem | Eigenvalue | Exponential convergence-tractability | Average case setting | KOROBOV SPACES | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | MULTIVARIATE INTEGRATION

Journal Article

Journal of Logic and Computation, ISSN 0955-792X, 2/2009, Volume 19, Issue 1, pp. 89 - 122

Recently it has been shown that the miniaturization mapping ℳ faithfully translates bexponential parameterized complexity into (unbounded) parameterized...

Miniaturization mapping | Exponential time complexity | Parameterized complexity | COMPUTER SCIENCE, THEORY & METHODS | exponential time complexity | miniaturization mapping | LOGIC | COMPLEXITY

Miniaturization mapping | Exponential time complexity | Parameterized complexity | COMPUTER SCIENCE, THEORY & METHODS | exponential time complexity | miniaturization mapping | LOGIC | COMPLEXITY

Journal Article

JOURNAL OF COMPLEXITY, ISSN 0885-064X, 08/2017, Volume 41, pp. 102 - 125

We study multivariate L-infinity-approximation for a weighted Korobov space of periodic functions for which the Fourier coefficients decay exponentially fast....

Multivariate L-infinity-approximation | MATHEMATICS | HILBERT-SPACES | MATHEMATICS, APPLIED | Worst-case error | Korobov spaces | Tractability Exponential convergence | TRACTABILITY | MULTIVARIATE INTEGRATION

Multivariate L-infinity-approximation | MATHEMATICS | HILBERT-SPACES | MATHEMATICS, APPLIED | Worst-case error | Korobov spaces | Tractability Exponential convergence | TRACTABILITY | MULTIVARIATE INTEGRATION

Journal Article

Journal of Complexity, ISSN 0885-064X, 02/2016, Volume 32, Issue 1, pp. 92 - 121

We are aiming at sharp and explicit-in-dimension estimations of the cardinality of s-dimensional hyperbolic crosses where s may be large, and applications in...

Tractability | High-dimensional approximation | Hyperbolic cross | [formula omitted]-dimensions | [formula omitted]-widths | Exponential tractability | ε-dimensions | N-widths | MATHEMATICS, APPLIED | NUMBER | GRIDS | SPACES | SPARSE FINITE-ELEMENTS | LATTICE POINTS | epsilon-dimensions | ELLIPTIC PROBLEMS | COMPUTER SCIENCE, THEORY & METHODS

Tractability | High-dimensional approximation | Hyperbolic cross | [formula omitted]-dimensions | [formula omitted]-widths | Exponential tractability | ε-dimensions | N-widths | MATHEMATICS, APPLIED | NUMBER | GRIDS | SPACES | SPARSE FINITE-ELEMENTS | LATTICE POINTS | epsilon-dimensions | ELLIPTIC PROBLEMS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 11/2017, Volume 231, pp. 211 - 216

In the Vertex Planarization problem one asks to delete the minimum possible number of vertices from an input graph to obtain a planar graph. The parameterized...

Vertex planarization | Exponential Time Hypothesis | Fixed-parameter tractability | Treewidth | MATHEMATICS, APPLIED | TIME | Algorithms

Vertex planarization | Exponential Time Hypothesis | Fixed-parameter tractability | Treewidth | MATHEMATICS, APPLIED | TIME | Algorithms

Journal Article

Journal of Complexity, ISSN 0885-064X, 08/2017, Volume 41, pp. 102 - 125

We study multivariate L∞-approximation for a weighted Korobov space of periodic functions for which the Fourier coefficients decay exponentially fast. The...

Tractability | Exponential convergence | Worst-case error | Korobov spaces | Multivariate [formula omitted]-approximation | approximation | Multivariate L | Algorithms

Tractability | Exponential convergence | Worst-case error | Korobov spaces | Multivariate [formula omitted]-approximation | approximation | Multivariate L | Algorithms

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 07/2016, Volume 207, pp. 98 - 126

We consider L2-approximation of elements of a Hermite space of analytic functions over Rs. The Hermite space is a weighted reproducing kernel Hilbert space of...

Tractability | Hermite spaces | Exponential convergence | Multivariate approximation | MATHEMATICS | WEIGHTED KOROBOV SPACES | MULTIVARIATE INTEGRATION | Algorithms

Tractability | Hermite spaces | Exponential convergence | Multivariate approximation | MATHEMATICS | WEIGHTED KOROBOV SPACES | MULTIVARIATE INTEGRATION | Algorithms

Journal Article

Methods in Molecular Biology, ISSN 1064-3745, 2017, Volume 1526, pp. 363 - 402

Fixed-parameter algorithms are designed to efficiently find optimal solutions to some computationally hard (NP-hard) problems by identifying and exploiting...

Discrete problems | Optimal solutions | Exponential running times | NP-hard problems | Algorithm design | Computational intractability | Fixed-parameter tractability | Computational Biology - methods | Algorithms

Discrete problems | Optimal solutions | Exponential running times | NP-hard problems | Algorithm design | Computational intractability | Fixed-parameter tractability | Computational Biology - methods | Algorithms

Journal Article

Mathematics and Computers in Simulation, ISSN 0378-4754, 01/2018, Volume 143, pp. 35 - 45

We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine...

Worst-case error | Numerical integration | Function approximation | Exponential convergence-Tractability | Cosine space | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MULTIVARIATE INTEGRATION

Worst-case error | Numerical integration | Function approximation | Exponential convergence-Tractability | Cosine space | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MULTIVARIATE INTEGRATION

Journal Article

ACM Transactions on Computation Theory (TOCT), 05/2018, Volume 10, Issue 2, pp. 1 - 32

The H - free E dge D eletion problem asks, for a given graph G and integer k , whether it is possible to delete at most k edges from G to make it H -free-that...

H -free graphs | fixed-parameter tractability | Hardness of approximation | exponential time hypothesis | graph modification problems

H -free graphs | fixed-parameter tractability | Hardness of approximation | exponential time hypothesis | graph modification problems

Journal Article

SIAM Journal on Computing, ISSN 0097-5397, 2013, Volume 42, Issue 3, pp. 1218 - 1244

The P vs. NP problem arose from the question of whether exhaustive search is necessary for problems with short verifiable solutions. We do not know if even a...

Time-space trade-offs | Improved exponential algorithms | Lower bounds | Circuit complexity | Exact algorithms | circuit complexity | MATHEMATICS, APPLIED | SPACE TRADEOFFS | PROOFS | NONDETERMINISM | POLYNOMIAL-TIME HIERARCHY | improved exponential algorithms | SAT | COMPLEXITY THEORY | ALGORITHMS | CIRCUIT LOWER BOUNDS | FIXED-PARAMETER TRACTABILITY | lower bounds | time-space trade-offs | exact algorithms | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Computer simulation | Computation | Searching | Mathematical analysis | Mathematical models | Extreme values

Time-space trade-offs | Improved exponential algorithms | Lower bounds | Circuit complexity | Exact algorithms | circuit complexity | MATHEMATICS, APPLIED | SPACE TRADEOFFS | PROOFS | NONDETERMINISM | POLYNOMIAL-TIME HIERARCHY | improved exponential algorithms | SAT | COMPLEXITY THEORY | ALGORITHMS | CIRCUIT LOWER BOUNDS | FIXED-PARAMETER TRACTABILITY | lower bounds | time-space trade-offs | exact algorithms | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Computer simulation | Computation | Searching | Mathematical analysis | Mathematical models | Extreme values

Journal Article

Leibniz International Proceedings in Informatics, LIPIcs, ISSN 1868-8969, 09/2017, Volume 87

Conference Proceeding

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