We present a new method to compress matrices based on interpolatory mu
ltiresolution. The matrices so compressed allow all kinds of algebraic
operations, including matrix-matrix multiplication. We illustrate thr
ough examples the performance of the compressed matrices. We call the
form devised here standard in contrast to the nonstandard form introdu
ced by Harten and Yad-Shalom in previous papers, because they are the
interpolatory multiresolution equivalent to the standard and nonstanda
rd wavelet forms, respectively.