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We present an efficient and scalable algorithm for performing matrix-vector multiplications ("matvecs") for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving…
Scanning exhaustively a big data matrix DM for subsets of independent variables IVs that are associated with a dependent variable DV is computationally tractable only for 1- and 2-IV effects. I present a highly computationally tractable…
Image reconstruction in Magnetic Resonance Imaging (MRI) is fundamentally a linear inverse problem, such that the image can be recovered via explicit pseudoinversion of the encoding matrix by solving $\textbf{data} = \textbf{Encode} \times…
Calculating the inverse kinematics (IK) is a fundamental challenge in robotics. Compared to numerical or learning-based approaches, analytical IK provides higher efficiency and accuracy. However, existing analytical approaches are difficult…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
Highly concentrated functions play an important role in many research fields including control system analysis and physics, and they turned out to be the key idea behind inverse Laplace transform methods as well. This paper uses the…
A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x…
In this paper, we propose a new primal-dual algorithm for minimizing $f(x) + g(x) + h(Ax)$, where $f$, $g$, and $h$ are proper lower semi-continuous convex functions, $f$ is differentiable with a Lipschitz continuous gradient, and $A$ is a…
We present two algorithms for computing hypergeometric solutions of second order linear differential operators with rational function coefficients. Our first algorithm searches for solutions of the form \[ \exp(\int r \,…
This paper presents an algorithm for computing Sine-Cosine pairs to modest accuracy, but in a manner which contains no conditional tests or branching, making it highly amenable to vectorization. An exemplary implementation for PowerPC…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
An algorithm is presented for generating successive approximations to trigonometric functions of sums of non-commuting matrices. The resulting expressions involve nested commutators of the respective matrices. The procedure is shown to…
We present a method for computing actions of the exponential-like $\varphi$-functions for a Kronecker sum $K$ of $d$ arbitrary matrices $A_\mu$. It is based on the approximation of the integral representation of the $\varphi$-functions by…
In this paper we propose an accurate, highly parallel algorithm for the generalized eigendecomposition of a matrix pair $(H, S)$, given in a factored form $(F^{\ast} J F, G^{\ast} G)$. Matrices $H$ and $S$ are generally complex and…
We exhibit a randomized algorithm which given a matrix $A\in \mathbb{C}^{n\times n}$ with $\|A\|\le 1$ and $\delta>0$, computes with high probability an invertible $V$ and diagonal $D$ such that $\|A-VDV^{-1}\|\le \delta$ using…
Being inspired by phasor analysis in linear circuit theory, and its algebraic counterpart - the AC-(operational)-calculus for sinusoids developed by W. Marten and W. Mathis - we define a complex structure on several spaces of real-valued…
Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable…
We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
We introduce the atomic valence active space (AVAS), a simple and well-defined automated technique for constructing active orbital spaces for use in multi-configuration and multireference (MR) electronic structure calculations. Concretely,…