Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on thei...Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on theinterval [a,b], α_j β_j are extended real numbers satisfying α_j<+∞, β_j>? andα_j≤β_j. Assumethat f is a continuous function defined on a compact set X [a, b]. This paper gives the characterizationtheorem for p being the best uniform approximation to f from K, and points out that the characteri-zation theorem can be applied in calculating the approximate solution of best approximation to f fromK.展开更多
文摘Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on theinterval [a,b], α_j β_j are extended real numbers satisfying α_j<+∞, β_j>? andα_j≤β_j. Assumethat f is a continuous function defined on a compact set X [a, b]. This paper gives the characterizationtheorem for p being the best uniform approximation to f from K, and points out that the characteri-zation theorem can be applied in calculating the approximate solution of best approximation to f fromK.
