Ten lectures on wavelets
On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
Convergence of iterations for linear equations
Convergence of iterations for linear equations
Using the refinement equation for evaluating integrals of wavelets
SIAM Journal on Numerical Analysis
Wavelet-like bases for the fast solutions of second-kind integral equations
SIAM Journal on Scientific Computing
An introduction to wavelets
Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions
SIAM Journal on Numerical Analysis
A Multiresolution Approach to Regularization of Singular Operators and Fast Summation
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
On the best approximation of function classes from values on a uniform grid in the real line
ICOSSE'06 Proceedings of the 5th WSEAS international conference on System science and simulation in engineering
Solving Volterra integral equations of the second kind by wavelet-Galerkin scheme
Computers & Mathematics with Applications
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For the Fredholm integral equation u = Tu + f on the real line, fast solvers are designed on the basis of a discretized wavelet Galerkin method with the Sloan improvement of the Galerkin solution. The Galerkin system is solved by GMRES or by the Gauss elimination method. Our concept of the fast solver includes the requirements that the parameters of the approximate solution un can be determined in O(n*) flops and the accuracy ||u - un||0,b ≤ cn*-m||f(m)||0,a is achieved where n* = n*(n) is the number of sample points at which the values of f and K, the kernel of the integral operator, are involved; moreover, we require that, having determined the parameters of un, the value of un at any particular point x ∈ (-∞, ∞) is available with the same accuracy O(n*-m) at the cost of O(1) flops. Here || ċ ||0,a and || ċ ||0,b are certain weighted uniform norms. Using GMRES, the 2m-smoothness of K is sufficient; in case of Gauss method, K must be smoother.