The computational complexity of differential and integral equations: an information-based approach

SIGACT news complexity theory column 31

ACM SIGACT News

Complexity theory for lie-group solvers

Journal of Complexity

Complexity of nonlinear two-point boundary-value problems

Journal of Complexity

Where does smoothness count the most for Fredholm equations of the second kind with noisy information?

Journal of Complexity

Information-based complexity

Encyclopedia of Computer Science

The randomized information complexity of elliptic PDE

Journal of Complexity

The Quantum Setting with Randomized Queries for Continuous Problems

Quantum Information Processing

Optimal approximation of elliptic problems by linear and nonlinear mappings I

Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004

Optimal approximation of elliptic problems by linear and nonlinear mappings II

Journal of Complexity

The quantum query complexity of elliptic PDE

Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005

Computability of Solutions of Operator Equations

Electronic Notes in Theoretical Computer Science (ENTCS)

Tractability of quasilinear problems I: General results

Journal of Approximation Theory

Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian Eigenmaps

Proceedings of the 24th international conference on Machine learning

Note: A note on the complexity and tractability of the heat equation

Journal of Complexity

Optimal recovery of solutions of the generalized heat equation in the unit ball from inaccurate data

Journal of Complexity

Multivariate L∞ approximation in the worst case setting over reproducing kernel Hilbert spaces

Journal of Approximation Theory

Adaptivity and computational complexity in the numerical solution of ODEs

Journal of Complexity

Linear information versus function evaluations for L2-approximation

Journal of Approximation Theory

On the power of standard information for multivariate approximation in the worst case setting

Journal of Approximation Theory

New averaging technique for approximating weighted integrals

Journal of Complexity

Optimal approximation of elliptic problems by linear and nonlinear mappings IV: Errors in L2 and other norms

Journal of Complexity

Tractability of the Helmholtz equation with non-homogeneous Neumann boundary conditions: The relation to the L2-approximation

Journal of Complexity

Optimal approximation of elliptic problems by linear and nonlinear mappings I

Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004

The randomized information complexity of elliptic PDE

Journal of Complexity