A class of bases in L2 for the sparse representations of integral operators
SIAM Journal on Mathematical Analysis
Wavelet Galerkin methods for second-kind integral equations
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Multiwavelets for Second-Kind Integral Equations
SIAM Journal on Numerical Analysis
The Petrov--Galerkin and Iterated Petrov--Galerkin Methods for Second-Kind Integral Equations
SIAM Journal on Numerical Analysis
A construction of interpolating wavelets on invariant sets
Mathematics of Computation
Digital Image Processing
Fast Collocation Methods for Second Kind Integral Equations
SIAM Journal on Numerical Analysis
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This paper studies the data redundancy of the coefficient matrix of the corresponding discrete system which forms a basis for fast algorithms of solving the integral equation whose kernel includes a convolution function factor. We develop lossless matrix compression strategies, which reduce the cost of integral evaluations and the storage to linear complexity, i.e., the same order of the approximation space dimensions. We establish that this algorithm preserves the convergence order of the approximate solution. We also propose a hardware-aware parallel algorithm for these strategies.