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a binomial is a polynomial that is the sum of two terms, each of which is a monomial. It is the simplest kind of a sparse polynomial after the monomials...

roots of a polynomial are the roots of the GCD of the polynomial and its derivative, and further GCD computations allow computing the square-free factorization...

exists a sparse language that is P-complete, then L = P. P is contained in BQP, it is unknown whether the containment is strict. Polynomial-time algorithms...

positive square numbers, or as the values of a cubic polynomial. They can be used to solve several other counting problems, including counting squares in a...

perfect square modulo some integer Quadratic function – Polynomial function of degree two Square triangular number – Integer that is both a perfect square and...

certain polynomials, those polynomials should have the polynomial SOS property. When fixing the maximum degree of the polynomials involved, sum-of-squares optimization...

probabilistic polynomial identity testing. Identity testing is the problem of determining whether a given multivariate polynomial is the 0-polynomial, the polynomial...

Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and...

data-sparse approximation of a non-sparse matrix Hilbert matrix, a square matrix with entries being the unit fractions Hollow matrix, a square matrix...

it has a nonzero determinant and the eigenvalues of a square matrix are the roots of a polynomial determinant. In geometry, matrices are widely used for...

Birkhoff introduced the chromatic polynomial to study the coloring problem, which was generalised to the Tutte polynomial by W. T. Tutte, both of which are...

Sparse identification of nonlinear dynamics (SINDy) is a data-driven algorithm for obtaining dynamical systems from data. Given a series of snapshots of...

(2004) study polynomial analogues of the square triangular number formula, in which series of polynomials add to the square of another polynomial. Sloane,...

; Güntürk, C. S. N. (2010). "Iteratively reweighted least squares minimization for sparse recovery". Communications on Pure and Applied Mathematics....

convergence of a series Aitken's delta-squared process — most useful for linearly converging sequences Minimum polynomial extrapolation — for vector sequences...

pseudo-polynomial time algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time...

number field sieve is super-polynomial but sub-exponential in the size of the input. Suppose f is a k-degree polynomial over Q {\textstyle \mathbb {Q}...

of a polynomial with degree 5 or more. (Generality matters because any polynomial with degree n {\displaystyle n} is the characteristic polynomial of some...

computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce the complexity...

interpolating functions are polynomials. In practice, since polynomials of very high degree tend to oscillate wildly, only polynomials of low degree are used...