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Results for “matrix algebra”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1982

Assessing the quality of curvilinear coordinate meshes by decomposing the Jacobian matrix

An algebraic decomposition of the Jacobian matrix which relates physical and computational variables is presented. This invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation, cell orthogonality, cell volume, and cell aspect ratio. The decomposition can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm. This is worked out in detail for Laplace's equation in nonconservative and conservative forms. The analysis is applied to the solution of the full potential code TAIR, showing grid plots, carpet plots, and truncation error for a NACA 0012 airfoil.

Kerlick, G. D.↗

NASA NTRS1966

Inverse of the Vandermonde matrix with applications

Inverse of Vandermonde matrix with applications

MATRIX ALGEBRA↗

NASA NTRS1965

Matrix methods for calculating zeros, coefficients, Christoffel numbers, and derivatives of some orthogonal polynomials

Jacobi matrix method for calculating zeros, coefficients, Christoffel numbers, and derivatives of orthogonal polynomials

MATRIX ALGEBRA↗

NASA NTRS1966

Bimodules for composition algebras.

Construction of Cayley-Dickson type and involution type bimodules for composition algebras

COMPOSITE FUNCTION↗

NASA NTRS1966

Permutation-algebraic formulation of spin-free transition density matrices.

Spin-free transition density matrices, using permutation group algebra

DENSITY↗

NASA NTRS1981

Iterative optical vector-matrix processors (survey of selected achievable operations)

An iterative optical vector-matrix multiplier with a microprocessor-controlled feedback loop capable of performing a wealth of diverse operations was described. A survey and description of many of its operations demonstrates the versatility and flexibility of this class of optical processor and its use in diverse applications. General operations described include: linear difference and differential equations, linear algebraic equations, matrix equations, matrix inversion, nonlinear matrix equations, deconvolution and eigenvalue and eigenvector computations. Engineering applications being addressed for these different operations and for the IOP are: adaptive phased-array radar, time-dependent system modeling, deconvolution and optimal control.

Casasent, D.↗

NASA NTRS1963