# Where Does Smoothness Count the Most for Two-Point Boundary-Value Problems?

@article{Werschulz1999WhereDS, title={Where Does Smoothness Count the Most for Two-Point Boundary-Value Problems?}, author={Arthur G. Werschulz}, journal={J. Complex.}, year={1999}, volume={15}, pages={360-384} }

Abstract We study the complexity of scalar 2 m th order elliptic two-point boundary-value problems Lu = f , error being measured in the energy norm. Previous work on the complexity of these problems has generally assumed that we had partial information about the right-hand side f and complete information about the coefficients of L . In this paper, we study the complexity of such problems when, in addition to partial information about f , we have only partial information about the coefficients…

## 2 Citations

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

- Computer ScienceJ. Complex.
- 2003

### Complexity of Nonlinear Two-Point Boundary-Value Problems

- Computer Science, MathematicsJ. Complex.
- 2002

We study upper and lower bounds on the worst-case e-complexity of nonlinear two-point boundary-value problems. We deal with general systems of equations with general nonlinear boundary conditions, as…

## References

SHOWING 1-10 OF 17 REFERENCES

### The Complexity of Definite Elliptic Problems with Noisy Data

- Computer ScienceJ. Complex.
- 1996

We study the complexity of 2mth order definite elliptic problemsLu=f(with homogeneous Dirichlet boundary conditions) over ad-dimensional domain ?, error being measured in theHm(?)-norm. The problem…

### Information-Based Complexity

- Computer Science
- 1988

This book provides a comprehensive treatment of information-based complexity, the branch of computational complexity that deals with the intrinsic difficulty of the approximate solution of problems…

### Information-based complexity

- Computer ScienceNature
- 1987

Information-based complexity seeks to develop general results about the intrinsic difficulty of solving problems where available information is partial or approximate and to apply these results to…

### The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

- Mathematics
- 1972

### Computational complexity of differential and integral equations - an information-based approach

- Mathematics, Computer ScienceOxford mathematical monographs
- 1991

This book discusses elliptic boundary value problems, linear elliptic systems, and some basic measure theory results for the average case setting.

### Survey lectures on the mathematical foundations of the nite element method, The Mathematical Foundations of the Finite Element Method With Applications to Partial Diierential Equations

- Survey lectures on the mathematical foundations of the nite element method, The Mathematical Foundations of the Finite Element Method With Applications to Partial Diierential Equations
- 1972

### Constructive Approximation: Advanced Problems, Grund lehren der mathematischen Wissenschaften 304

- 1996