This paper presents an efficient algorithm for computing the characteristic polynomial of a matrix, which utilizes Cayley-Hamilton’s theorem. The algorithm requires no condition on input matrix and can be performed only with basic matrix operations except only one computation of inverse of constant matrix. Though the algorithm can be applied to a constant matrix, it is the most effective when a...

We estimate the Lebesgue constants for Lagrange interpolation processes on one or several intervals by rational functions with fixed poles. admit that poles have finitely many accumulation points intervals. To prove it we use an analog of inverse polynomial image method

Inverse solutions to interpolation techniques in computer graphics may increase the accuracy of the rendered frames. An example is the use of an arbitrary time stamp in time interpolation to evaluate the t-parameter, which in turn can be used for time-variant spatial interpolation. In this paper, an analytic inverse is presented for a shape-preserving piecewise cubic Hermite interpolant, used i...

Inverse optimization is the problem of determining the values of missing input parameters that are closest to given estimates and that will make a given target solution optimal. This study is concerned with inverse mixed integer linear optimization problems (MILPs) in which the missing parameters are objective function coefficients. This class generalizes the class studied by Ahuja and Orlin [2...

It is well known that the degree-raised Bernstein-Bézier coefficients of degree n of a polynomial g converge to g at the rate 1/n. In this paper we consider the polynomial An(g) of degree ≤ n interpolating the coefficients. We show how An can be viewed as an inverse to the Bernstein operator and that the derivatives An(g) (r) converge uniformly to g at the rate 1/n for all r. We also give an as...

One may consider that the algebraic complexity of basic linear algebra over an abstract field K is well known. Indeed, if ω is the exponent of matrix multiplication over K, then for instance computing the determinant, the matrix inverse, the rank or the characteristic polynomial of an n×n matrix over K can be done in O (̃n) operations in K. Here the soft “O” notation indicates some missing logar...

It is known that some polynomial mappings φ : Ck → Cn are recti able in the sense that there exists a polynomial mapping α : Cn → Cn whose inverse is also polynomial and for which α(φ(z1, . . . , zk)) = (z1, . . . , zk, 0, . . . , 0) for all z1, . . . , zk. In many cases, the existence of such a recti cation is proven indirectly, without an explicit construction of the mapping α. In this paper,...