Related papers: The W. Thurston Algorithm Applied to Real Polynomi…
This article builds on Thurston's height functions. His tiling algorithm is reinterpreted using lattice theory and then generalized in order to generate any tiling of a hole-free region. Combined with a natural encoding of tilings by words,…
We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite number of…
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
We introduce a Whitney polynomial for hypermaps and use it to generalize the results connecting the circuit partition polynomial to the Martin polynomial and the results on several graph invariants.
We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients.…
Combinatorial $t$-designs have nice applications in coding theory, finite geometries and several engineering areas. There are two major methods of constructing $t$-designs. One of them is via group actions of certain permutation groups…
We extend Sullivan's complex a priori bounds to real quadratic polynomials with essentially bounded combinatorics. Combined with the previous results of the first author, this yields complex bounds for all real quadratics. Local…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating F, whose components satisfy the same relations.
We build a class of polynomial problems with not polynomial certificates. The parameter concerning which are defined efficiency of corresponding algorithms is the number $n$ of elements of the set has used at construction of combinatory…
Every rotationless outer automorphism of a finite rank free group is represented by a particularly useful relative train track map called a CT. The main result of this paper is that the constructions of CTs can be made algorithmic. A key…
According to the real \tau-conjecture, the number of real roots of a sum of products of sparse polynomials should be polynomially bounded in the size of such an expression. It is known that this conjecture implies a superpolynomial lower…
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichm\"uller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal…
By using the Poisson formula for resultants and the variants of chip-firing game on graphs, we provide a combinatorial method for computing a class of of resultants, i.e. the characteristic polynomials of the adjacency tensors of starlike…
We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental…
We present a set of new, efficient high-order symplectic methods designed for Hamiltonian systems with cubic or quartic potentials. By demonstrating that polynomial potentials require fewer order conditions, we develop schemes that…
This thesis deals with the enumerative study of combinatorial maps, and its application to the enumeration of other combinatorial objects. Combinatorial maps, or simply maps, form a rich combinatorial model. They have an intuitive and…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
The perception of high-definition maps is an integral component of environmental perception in autonomous driving systems. Existing research have often focused on online construction of high-definition maps. For instance, the Maptr[9]…