Related papers: A Closed-form Solution to the Wahba Problem for Pa…
Quaternions provide a unified algebraic and geometric framework for representing three-dimensional rotations without the singularities that afflict Euler-angle parametrisations. This article develops a pedagogical and conceptual analysis of…
We propose a least-squares formulation to the noisy hand-eye calibration problem using dual-quaternions, and introduce efficient algorithms to find the exact optimal solution, based on analytic properties of the problem, avoiding non-linear…
We present a numerical solution of the parquet approximation (PA), a conserving diagrammatic approach which is self-consistent at both the single-particle and the two-particle levels. The fully irreducible vertex is approximated by the bare…
This paper is about the old Wahba problem in its more general form, which we call "simultaneous rotation and correspondence search". In this generalization we need to find a rotation that best aligns two partially overlapping $3$D point…
Recently, Zhuang, Roth, \& Sudhakar [1] proposed a method that allows simultaneous computation of the rigid transformations from world frame to robot base frame and from hand frame to camera frame. Their method attempts to solve a…
In this paper, we present some numerical applications for the equation $x^2+ax+b=0$, where $a, b$ are two quaternionic elements in $\mathbb{H}(\alpha,\beta)$. Based on well-known solving methods, we have developed a new numerical algorithm…
In this paper, we provide a structure-preserving one-sided cyclic Jacobi method for computing the singular value decomposition of a quaternion matrix. In this method, the columns of the quaternion matrix are orthogonalized in pairs by using…
Horn's problem, i.e., the study of the eigenvalues of the sum $C=A+B$ of two matrices, given the spectrum of $A$ and of $B$, is re-examined, comparing the case of real symmetric, complex Hermitian and self-dual quaternionic $3\times 3$…
We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works…
We derive a charged black hole solution in four dimensions described by $SL(2,R)\times SU(2)\times U(1)/U(1)^2$ WZW coset model. Using the algebraic Hamiltonian method we calculate the corresponding solution that is exact to all orders in…
In this paper, we prove a conjecture which was presented in a recent paper [Linear Algebra Appl. 2016; 496: 549--593]. We derive some practical necessary and sufficient conditions for the existence of a solution to a system of coupled…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…
Peter Denton, Stephen Parke, Terence Tao and Xining Zhang [arxiv 2019] presented a basic and important identity in linear commutative algebra, so-called {\bf the eigenvector-eigenvalue identity} (formally named in [BAMS, 2021]), which is a…
All quaternion methods for static attitude determination currently rely on either the spectral decomposition of a 4 x 4 matrix (q-Method) or finding the maximum eigenvalue of a 4th-order characteristic equation (QUEST). Using a spectral…
Solving a quadratic equation $P(x)=ax^2+bx+c=0$ with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang and So \cite{Huang} give a complete set of formulas, breaking…
In this paper, we derive explicit formulas for computing the roots of $ax^{2}+bx+c=0$ with $a$ being not invertible in split quaternion algebra. We also imitate the approach developed by Opfer, Janovska and Falcao etc. to verify our results…
Sylvester-type matrix equations have applications in areas including control theory, neural networks, and image processing. In this paper, we establish the necessary and sufficient conditions for the system of Sylvester-type quaternion…
We develop observer design over hypercomplex quaternions in a characteristic-polynomial-free framework. Using the standard right-module convention, we derive a right observable companion form and companion polynomial that encode error…
Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et…
Quaternions are important for a wide variety of rotation-related problems in computer graphics, machine vision, and robotics. We study the nontrivial geometry of the relationship between quaternions and rotation matrices by exploiting the…