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We present a recursive minimal polynomial theorem for finite sequences over a commutative integral domain $D$. This theorem is relative to any element of $D$. The ingredients are: the arithmetic of Laurent polynomials over $D$, a recursive…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
In this paper, we derive new computational techniques for residue number systems (RNS) based Barrett algorithm (BA). The focus of the work is an algorithm that carries out the entire computation using only modular arithmetic without…
This paper gives the recursion formula for mixed multiplicities of maximal degrees with respect to joint reductions of ideals, which is one of important results in the mixed multiplicity theory. Using this result, we give consequences on…
Random residue sequences (RR) may be used in many random number applications including those related to multiple access in communications. This paper investigates variations on an algorithm to generate RR sequences that was proposed earlier…
Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting…
In recent years, there has been a remarkable development of simulation-based inference (SBI) algorithms, and they have now been applied across a wide range of astrophysical and cosmological analyses. There are a number of key advantages to…
We present a method for improving the performance of nested sampling as well as its accuracy. Building on previous work by Chen et al., we show that posterior repartitioning may be used to reduce the amount of time nested sampling spends in…
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 present a Poisson formula for sparse resultants and a formula for the product of the roots of a family of Laurent polynomials, which are valid for arbitrary families of supports. To obtain these formulae, we show that the sparse…
We extend our previous work on Poisson-like formulas for subresultants in roots to the case of polynomials with multiple roots in both the univariate and multivariate case, and also explore some closed formulas in roots for univariate…
Earlier versions proposed Graded Projection Recursion (GPR) as a deterministic packed-recursion framework for model-honest near-quadratic dense matrix multiplication. This revised version withdraws the exact dense matrix multiplication…
Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that…
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…
First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also…
High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension…
Reduced Rank Extrapolation (RRE) is a polynomial type method used to accelerate the convergence of sequences of vectors $\{\boldsymbol{x}_m\}$. It is applied successfully in different disciplines of science and engineering in the solution…
This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…
Pseudoinverses are ubiquitous tools for handling over- and under-determined systems of equations. For computational efficiency, sparse pseudoinverses are desirable. Recently, sparse left and right pseudoinverses were introduced, using…