The approximation of functions of several variables continues to be a difficult problem in scientific computing because many of the algorithms required for such problems have yet to be written. This monograph is written for a broad audience of computational mathematicians and statisticians concerned with the development of algorithms or the derivation of approximations from linear projections, of which the interpolating operators are an important example. As an aid to both researchers and students, a bibliography of more than 200 titles is included.

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'There are many ingredients necessary for a successful monograph. It should be enjoyable to read, it should teach, and it should inspire further research. I believe Cheney's book scores highly on all three points.' F. Deutsch, Mathematical Reviews

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