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  "body": "\n## Summary\n\nNonlinear approximation approximates a function by elements of a set that is not a linear space.\nA typical such set is the sums of $n$ terms chosen freely from a dictionary.\nThe approximant may adapt to the function, for example by placing spline knots or wavelets where the function is rough.\nTypical cases are [[n-term approximation|GEK0NP5WQM]], [[rational approximation|EHFQK1WXKS]], splines with free knots and neural networks.\nFor functions with isolated singularities it can be much more efficient than linear approximation with the same number of parameters.\n\n## Explanations\n\n### L1 human\n\nIn linear approximation the building blocks are fixed in advance, for example the polynomials of degree at most $n$.\nIn nonlinear approximation one first looks at the function and then picks the building blocks that suit it best.\nThe set of all such choices is not closed under addition: the sum of two $n$-term sums can have $2n$ terms.\nFor example, to approximate a function that is smooth except for one jump, one can put many small wavelets near the jump and few elsewhere.\n",
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