Algebraic Algorithms

Authored by: Ioannis Z. Emiris , Victor Y. Pan , Elias P. Tsigaridas

Computing Handbook

Print publication date:  May  2014
Online publication date:  May  2014

Print ISBN: 9781439898529
eBook ISBN: 9781439898536
Adobe ISBN:


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Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves, and surfaces. In this vast area, manipulation with matrices and polynomials is fundamental for modern computations in sciences and engineering. The list of the respective computational problems includes the solution of a polynomial equation and linear and polynomial systems of equations, univariate and multivariate polynomial evaluation, interpolation, factorization and decompositions, rational interpolation, computing matrix factorization and decompositions (which in turn include various triangular and orthogonal factorizations such as LU, PLU, QR, QRP, QLP, CS, LR, Cholesky factorizations, and eigenvalue and singular value decompositions), computation of the matrix characteristic and minimal polynomials, determinants, Smith and Frobenius normal forms, ranks, and (generalized) inverses, univariate and multivariate polynomial resultants, Newton’s polytopes, greatest common divisors (GCDS), and least common multiples as well as manipulation with truncated series and algebraic sets.

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