Wavelet methods

More about the book

Wavelets have traditionally been used in signal analysis and image compression, but their analytical capabilities are increasingly recognized in Numerical Analysis. This research monograph explores the application of wavelet methods to elliptic differential equations, focusing on boundary treatment and conditions. It discusses key issues relevant to the efficient numerical solution of these problems, including preconditioning, stable discretizations, compression of fully populated matrices, evaluation of non-integer or negative norms, and adaptive refinements based on A-posteriori error estimators. A control problem with an elliptic boundary serves as an example to illustrate the conceptual strengths of wavelet techniques. The author expresses gratitude to several individuals who contributed to the writing process, particularly Prof. Dr. Wolfgang Dahmen, whose influence and collaboration have been invaluable. The stimulating scientific environment at the Institut für Geometrie und Praktische Mathematik, RWTH Aachen, and the enjoyable partnership with Prof. Dr. Reinhold Schneider from the Technical University of Chemnitz are also acknowledged.