In this chapter, we introduce the general problem of optimal approximation of a linear operator by the value of another operator. The spline interpolating method helps us to solve this problem and to obtain numerical formulas of optimal approximation for a wide variety of functional spaces and linear operators. More exactly, it is possible when the reproducing kernels or mappings are known and effectively calculated. Besides, in these cases the exact estimates of errors on classes and extremal elements can be obtained, too.
KeywordsLinear Operator Optimal Approximation Variational Theory Prolongation Method Approximation Formula
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