ABSTRACT
Arithmetic manipulation with matrices and polynomials is a common subject for algebraic (or symbolic) and numerical computing. Typical computational problems in these areas include the solution of a polynomial equation and linear and polynomial systems of equations, univariate and multivariate polynomial evaluation, interpolation, factorization and decompositions, rational interpolation, computingmatrix factorization and decompositions (which include various triangular and orthogonal factorizations such as LU, PLU, QR, QRP, QLP, CS, LR, Cholesky factorizations and eigenvalue and singular value decompositions [SVD]), computation of the matrix characteristic and minimal polynomials, determinants, Smith and Frobenius normal forms, ranks, (generalized) inverses, univariate and multivariate polynomial resultants, Newton’s polytopes, and greatest common divisors and least common multiples as well as manipulation with truncated series and algebraic sets.
