Any continuous function on a closed interval can be approximated arbitrarily closely by one of these functions according to the Weierstrass approximation theorem.
A Sturm Chain is a sequence of these objects obtained by application of a modified form of Euclid's algorithm, and algebraic varieties are certain level sets of them. Every matrix M will yield zero when substituted into one of these functions generated by taking the determinant of M minus lambda times I according to the Cayley-Hamilton theorem. Any continuous function on a closed interval can be approximated arbitrarily closely by one of these functions according to the Weierstrass approximation theorem. Functions may be interpolated with the sets of these named for Chebyshev or Lagrange and there is no general algebraic solution to ones of degree five or higher and. For 10 points, name these functions with powers of x and coefficients, like the quadratic x squared plus two x plus 3.
A Sturm Chain is a sequence of these objects obtained by application of a modified form of Euclid's algorithm, and algebraic varieties are certain level sets of them.
polynomials