1. Calculating generalised inverse matrices

Glencross, Michael J.

doi:10.2307/3617888

Cited by 3 publications

(3 citation statements)

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“…Ax = b Now we have a singular matrix in (5) and, according to the results in [2], the generalised inverse of is the matrix , where…”

Section: The Generalised Inverse Of a Matrixmentioning

confidence: 99%

“…1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 Now is singular, and a straightforward application of the ideas in [2] then shows that…”

Section: The Generalised Inverse Of a Matrixmentioning

confidence: 99%

“…The idea of using the generalised inverse of a singular matrix to solve the matrix equation has been discussed in the earlier papers [1,2,3,4] in the Gazette. Here we discuss three simple geometric questions which are of interest in their own right, and which illustrate the use of the generalised inverse of a matrix.…”

Section: Introductionmentioning

confidence: 99%

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Singular matrices and pairwise-tangent circles

Beardon

2024

Math. Gaz.

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The idea of using the generalised inverse of a singular matrix A to solve the matrix equation Ax = b has been discussed in the earlier papers [1, 2, 3, 4] in the Gazette. Here we discuss three simple geometric questions which are of interest in their own right, and which illustrate the use of the generalised inverse of a matrix. The three questions are about polygons and circles in the Euclidean plane. We need not assume that a polygon is a simple closed curve, nor that it is convex: indeed, abstractly, a polygon is just a finite sequence (v1, …, vn) of its distinct, consecutive, vertices. It is convenient to let vn + 1 = v1 and (later) Cn + 1 = C1.

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“…Ax = b Now we have a singular matrix in (5) and, according to the results in [2], the generalised inverse of is the matrix , where…”

Section: The Generalised Inverse Of a Matrixmentioning

confidence: 99%

“…1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 Now is singular, and a straightforward application of the ideas in [2] then shows that…”

Section: The Generalised Inverse Of a Matrixmentioning

confidence: 99%

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Singular matrices and pairwise-tangent circles

Beardon

2024

Math. Gaz.

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A Generalized Newton Method for Homogenization of Hamilton--Jacobi Equations

Cacace¹,

Camilli²

2016

SIAM J. Sci. Comput.

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We propose a new approach to the numerical solution of cell problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming from the discretization of the corresponding cell problems. We show that our method is able to solve efficiently cell problems in very general contexts, e.g., for first and second order scalar convex and nonconvex Hamiltonians, weakly coupled systems, dislocation dynamics and mean field games, also in the case of more competing populations. A large collection of numerical tests in dimension one and two shows the performance of the proposed method, both in terms of accuracy and computational time.

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Unexpected groups

Brakes

1995

Math. Gaz.

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The reader should first try the following exercise, which motivates the later work. Exercise: Prove that the set of real matrices forms a group under the usual matrix multiplication. This exercise comes with a guarantee that it will provoke at least a doubletake when first encountered. The usual reaction is to protest that these matrices are obviously singular, or to complain that the identity is missing from the set. Of course those familiar with this example can feel suitably smug in their rapid dismissal of these criticisms, but what was your reaction the first time you saw it?

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1. Calculating generalised inverse matrices

Cited by 3 publications

References 1 publication

Singular matrices and pairwise-tangent circles

Singular matrices and pairwise-tangent circles

A Generalized Newton Method for Homogenization of Hamilton--Jacobi Equations

Unexpected groups

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