从门捷列夫到傅里叶
本文探讨了由门捷列夫发现、马尔可夫推广的不等式：若P(x)是n次实多项式且在[-1,1]上满足|P(x)|≤1，则|P'(x)|≤n²。对于三角多项式，伯恩斯坦证明该界可从n²降至n。
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The article discusses linear algebra concepts applied to polynomials, specifically the set P_n(ℝ) of real polynomials with degree ≤ n. It explores how these polynomials can be expressed using n+1 scalar coefficients and examines their properties as a vector space.
Lagrange interpolating polynomials provide a method to find a polynomial that perfectly fits a given set of distinct data points. The approach constructs a polynomial of degree at most n that passes through n+1 specified points. This technique is widely used in numerical analysis and approximation theory.