sparsöfn

Sparsöfn is a term used in mathematics and computer science to describe a function whose nonzero values are confined to a small subset of its domain, making it sparse with respect to a chosen representation. The term is a neologism appearing in niche texts and online discussions, and it is not part of a formal standard nomenclature. In formal terms, a function f: X -> R is a sparsöfn with respect to a basis B if its coefficient vector representing f in B has relatively few nonzero entries.

The property of sparsöfn is often described as sparse support: there exists a subset S of indices, with small cardinality, such that f(x) = 0 for all x outside S. In practice, sparsöfns are represented by sparse vectors or sparse matrices, enabling efficient storage and computation. Under linear operations, the sparsöfn property may be preserved under certain conditions, for example, when combining sparse functions with disjoint supports.

Typical examples include digital signals that have only a few nonzero samples, or the wavelet or Fourier coefficients of a signal in which only a small number of coefficients are significant. In data science, sparsöfn concepts appear in compressed sensing, sparse coding, and model pruning, where exploiting sparsity reduces complexity.

Because sparsöfn is informal and not standardized, different authors may use it with slightly different meanings; in formal contexts, terms such as sparse function, sparse representation, or functions with sparse support are preferred. See also: sparsity; sparse representation; compressed sensing; wavelet; basis; support.