Numerical methods for design sensitivity analysis of multibody dynamics are presented. An analysis of the index-3 adjoint differential-algebraic equations is conducted and stability of the integration of the adjoint differential-algebraic equations in the backward direction is proven. Stabilized index-1 formulations are presented and convergence of backward differentiation formulas is shown for...

We had assembled a Java package, known as MatrixPak, of four classes for the purpose of numerical matrix computation. The classes are matrix, matrix_operations, StrToMatrix, and MatrixToStr; all of which are inherited from java.lang.Object class. Class matrix defines a matrix as a two-dimensional array of float types, and contains the following mathematical methods: transpose, adjoint, determin...

New definitions of determinant functionals over the quaternion skew field are given in this paper. The inverse matrix over the quaternion skew field is represented by analogues of the classical adjoint matrix. Cramer rule for right and left quaternionic systems of linear equations have been obtained.

Recently, a fast approximate algorithm for the evaluation of expansions in terms of standard L2 ( S2 ) -orthonormal spherical harmonics at arbitrary nodes on the sphere S2 has been proposed in [S. Kunis and D. Potts. Fast spherical Fourier algorithms. J. Comput. Appl. Math., 161:75 – 98, 2003]. The aim of this paper is to develop a new fast algorithm for the adjoint problem which can be used to...

Motivated by recent theoretical results obtained by the third author for the identification problem arising in single-photon emission computerized tomography (SPECT), we propose an adjoint state method for recovering both the source and the attenuation in the attenuated X-ray transform. Our starting point is the transport-equation characterization of the attenuated X-ray transform, and we apply...

We obtain oscillation criteria for a second order self-adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function. We illustrate our results with some nontrivial examples.

This report presents probability inequalities for sums of adapted sequences of random, self-adjoint matrices. The results frame simple, easily verifiable hypotheses on the summands, and they yield strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. The methods also specialize to sums of independent random matrices. 1. Main Results This technical report is...

where Idn is the n×n identity matrix in R, andA = (aij). We can’t quite invert this matrix, but we almost can. Recall that any n×nmatrixM has an adjoint matrix adj(M) such that adj(M)M = det(M)Idn. The coefficients of adj(M) are polynomials in the coefficients of M. (You’ve likely seen this in the form of a formula for M when there is an inverse.) Multiplying both sides of (1) on the left by ad...

By a generalized inverse of a given matrix, we mean a matrix that exists for a larger class of matrices than the nonsingular matrices, that has some of the properties of the usual inverse, and that agrees with inverse when given matrix happens to be nonsingular. In theory, there are many different generalized inverses that exist. We shall consider the Moore Penrose, weighted Moore-Penrose, Draz...