Reconstruction Kernel Space Numerical Analysis

Author: Cui Minggen
Publisher:
Publish Date: 2004-01-01
Features: This book is suitable for graduate students, teachers, and researchers in mathematics at comprehensive universities and institutions of higher learning, as well as for engineering technicians engaged in scientific and engineering computations. It proposes a special Hilbert space—the reproducing kernel Hilbert space—as an ideal framework for solving numerical analysis problems.
Chapter 1 introduces the theory of reproducing kernel Hilbert spaces;
Chapters 2 and 3 discuss interpolation problems, constructing one-dimensional and multivariate interpolation formulas that guarantee uniform convergence without derivative conditions for scattered node systems;
Chapter 4 discusses interpolation iteration methods;
Chapters 5 and 6 discuss various operator equations and their expressions based on the exact solutions of the equations, providing methods for solving numerical solutions;
Chapter 7 discusses functional extremal problems, giving expressions for the optimal solutions of a class of numerical functional problems;
Chapter 8 discusses an important class of nonlinear operator equations, providing expressions for their exact solutions.