On the computational complexity of ordinary differential equations
Information and Control
Complexity theory of real functions
Complexity theory of real functions
Computability structure of the Sobolev spaces and its applications
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
The Inversion Problem for Computable Linear Operators
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Computability theory of generalized functions
Journal of the ACM (JACM)
Computing with sequences, weak topologies and the axiom of choice
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Computability of Solutions of Operator Equations
Electronic Notes in Theoretical Computer Science (ENTCS)
On Computable Compact Operators on Banach Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
Computable Riesz Representation for Locally Compact Hausdorff Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
Are unbounded linear operators computable on the average for Gaussian measures?
Journal of Complexity
On the Effective Existence of Schauder Bases
Electronic Notes in Theoretical Computer Science (ENTCS)
Applied Numerical Mathematics
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We present computable versions of the Frechet-Riesz Representation Theorem and the Lax-Milgram Theorem. The classical versions of these theorems play important roles in various problems of mathematical analysis, including boundary value problems of elliptic equations. We demonstrate how their computable versions yield computable solutions of the Neumann and Dirichlet boundary value problems for a simple non-symmetric elliptic differential equation in the one-dimensional case. For the discussion of these elementary boundary value problems, we also provide a computable version of the Theorem of Schauder, which shows that the adjoint of a computably compact operator on Hilbert spaces is computably compact again.