Related papers: On the Inverting of A General Heptadiagonal Matrix
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
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…
A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…
We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…
We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…
This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian…
The inverse power method is a numerical algorithm to obtain the eigenvectors of a matrix. In this work, we develop an iteration algorithm, based on the inverse power method, to numerically solve the Schr\"odinger equation that couples an…
In many applications, it makes sense to solve the least square problems with nonnegative constraints. In this article, we present a new multiplicative iteration that monotonically decreases the value of the nonnegative quadratic programming…
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…
This paper introduces a general framework for iterative optimization algorithms and establishes under general assumptions that their convergence is asymptotically geometric. We also prove that under appropriate assumptions, the rate of…
A well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal $a$ on the diagonal and $b$ on the extra diagonals ($a, b\in \mathbb R$). The inverses of such matrices are…
Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such estimators for conjugate gradient algorithms used to solve…
We study the Reverse algorithm, a multidimensional continued fraction algorithm, which is not unimodular. We show that the Reverse algorithm is ergodic and, by proving that its second Lyapunov exponent is negative, that it is a.e.…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
In this paper, we discuss numerical methods for the eigenvalue decomposition of real symmetric matrices. While many existing methods can compute approximate eigenpairs with sufficiently small backward errors, the magnitude of the resulting…
The computation of generalized inverses of quaternion matrices is a fundamental problem in quaternion linear algebra, with wide-ranging applications in signal processing, image restoration, and multidimensional data analysis. This paper…