Fast algorithms for integral equations.

by Wing-Fai Ng.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 7-8).Abstract --- p.1-2Introduction --- p.3-6References --- p.7-8Paper I --- p.9-32Paper II --- p.33-6

Fast algorithm for ill-conditioned toeplitz and toeplitz-like systems.

by Hai-Wei Sun.Thesis (Ph.D.)--Chinese University of Hong Kong, 1996.Includes bibliographical references.Abstracts --- p.1Summary --- p.3Introduction --- p.3Summary of the papers A-C --- p.5Paper A --- p.19Paper B --- p.34Paper C --- p.6

A fast and well-conditioned spectral method for singular integral equations

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in ${\cal O}(m^2n)$ operations using an adaptive QR factorization, where $m$ is the bandwidth and $n$ is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to ${\cal O}(m n)$ operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The Julia software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface

Fast Numerical Methods for Non-local Operators

[no abstract available

Numerical solution of integral equation of the second kind.

by Chi-Fai Chan.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 53-54).Abstract also in Chinese.Chapter Chapter 1 --- INTRODUCTION --- p.1Chapter §1.1 --- Polynomial Interpolation --- p.1Chapter §1.2 --- Conjugate Gradient Type Methods --- p.6Chapter §1.3 --- Outline of the Thesis --- p.10Chapter Chapter 2 --- INTEGRAL EQUATIONS --- p.11Chapter §2.1 --- Integral Equations --- p.11Chapter §2.2 --- Numerical Treatments of Second Kind Integral Equations --- p.15Chapter Chapter 3 --- FAST ALGORITHM FOR SECOND KIND INTEGRAL EQUATIONS --- p.20Chapter §3.1 --- Introduction --- p.20Chapter §3.2 --- The Approximation --- p.24Chapter §3.3 --- Error Analysis --- p.35Chapter §3.4 --- Numerical Examples --- p.40Chapter §3.5 --- Concluding Remarks --- p.51References --- p.5

Some fast algorithms in signal and image processing.

Kwok-po Ng.Thesis (Ph.D.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 138-139).AbstractsSummaryIntroduction --- p.1Summary of the papers A-F --- p.2Paper A --- p.15Paper B --- p.36Paper C --- p.63Paper D --- p.87Paper E --- p.109Paper F --- p.12