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A new method has been developed for compressing the matrices that occur in most integral-equation-based computer programs. This method is easy to interface with existing computer programs, and allows them to run significantly faster and with significantly less memory. This method applies not only to electromagnetic and acoustic computation, but also to most programs involving a Green's function or any integral equation with a kernel having some smoothness properties. Our numerical computations, running on a high-end personal computer, have achieved compression ratios of fifty times, and compressed inversion of the matrices fifty times faster than by previous methods. For larger problems, solved on high-performance computers, these ratios would improve to about one thousand to one for larger moment method problems.