Fast computation of approximant bases in canonical form
نویسندگان
چکیده
منابع مشابه
Fast computation of approximant bases in canonical form
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix multiplication: most other fast approximant basis algorithms basically aim at efficiently reducing the input instance to instances for which PMBasis is fast. Such red...
متن کاملCertification of minimal approximant bases
Considering a given computational problem, a certificate is a piece of additional data that one attaches to the output in order to help verifying that this output is correct. Certificates are often used to make the verification phase significantly more efficient than the whole (re-)computation of the output. Here, we consider the minimal approximant basis problem, for which the fastest known al...
متن کاملNotes on computing minimal approximant bases
When s = 1 and N = ‖n‖ − 1 this is the classical Hermite Padé approximation problem. Here we allow N to be arbitrary. We describe algorithms for computing an order N genset of type n: a matrix V ∈ k[x]∗×m such that every row of V is a solution to (1) and every solution P of (1) can be expressed as a k[x]-linear combination of the rows of V . Ideally, V will be a minbasis of solutions: V has ful...
متن کاملFast Computation of a Complex Quadratic Form
with t t t j ε ε ε Im Re + = , where } {Re t ε and } {Im t ε are independent real Gaussian white noise processes each with zero mean and variance 2 2 σ . These processes have been widely used to model the noise component in data models consisting of a deterministic signal and an additive noise. The pure harmonic signal, the damped harmonic signal, and the polynomial phase signal can be given as...
متن کاملComputation of a canonical form for linear differential-algebraic equations
This paper describes how a commonly used canonical form for linear differential-algebraic equations can be computed using numerical software from the linear algebra package LAPACK. This makes it possible to automate for example observer construction and parameter estimation in linear models generated by a modeling language like Modelica.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2020
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2019.07.011