We present a unifying approach to discrete Gabor analysis, based on unitary matrix factorization. The factorization point of view is notably useful for the design of efficient numerical algorithms. This presentation is the first systematic account of its kind. In particular, it is shown that ...
What is the condition number of the coefficient matrix in terms of the singular values of A? Hint: Use the SVD of A. Give an explicit expression for the inverse of the coefficient matrix, as a block 2-by-2 matrix. Hint: Use 2-by-2 block Gaussian elimination. Where have we previously...
>>> a = Matrix2x2([1,1,1,0]) >>> a Matrix2x2 object: [ 1 1 ] [ 1 0 ] So lets raise it first to a small power, and see how the two algorithms perform… >>> val = bin_pow(a,10,lsb=True,verbose=True,timer_loops=100) Call to bin_pow took: 2.84952e-05 sec. (min...
Some applications actually do a lot of computation very near zero. This is common in algorithms computing residuals or differential corrections. For maximum numerically safe performance, perform the key computations in extended precision arithmetic. If the application is a single-precision application, yo...
The numerical methods implemented by F# for Numerics include linear algebra algorithms such as matrix decomposition, descriptive statistics, curve fitting and regression, as well as spectral methods such as FFT. The visualization library provides an easy-to-use API that can be used interactively from...
We present a unifying approach to discrete Gabor analysis, based on unitary matrix factorization. The factorization point of view is notably useful for the design of efficient numerical algorithms. This presentation is the first systematic account of its kind. In particular, it is shown that differe...
Numerical Algorithms for Finite Element Computations on Concurrent Processors. Semiannual Report March 1, 1986-August 31, 1986.Numerical Algorithms for Finite Element Computations on Concurrent Processors. Semiannual Report March 1, 1986-August 31, 1986.Concurrent processingFinite...
aheadalgorithmsAcronymsBBHBojanczyk;BrendeHoogSweet:GKstructuredmatrix,eplitz-typermutationmatrix,ertriangular,uppertriangular,orthogonal.ErrorBoundsStructureStructuredmatricesquationwhicsomesimplestructure(usuallybanded,fewerfulldiagonals),respectivelysome(small)g-generatorg-displacementcaseswheresmall(sabasicclassesmatrices...
1. MATHEMATICAL PRELIMINARIES AND ERROR ANALYSIS. Review of Calculus. Round-off Errors and Computer Arithmetic. Algorithms and Convergence. Numerical Software and Chapter Summary. 2. SOLUTIONS OF EQUATIONS IN ONE VARIABLE. The Bisection Method. Fixed-Point Iteration. Newton's Method and Its Extensions...
A sparse factorization for quasi-Newton type methods has been obtained. Algorithms for solving combined systems of linear and non-linear algebraic equations and matrix splitting have also been developed. A new algorithm has been found for updating the sparse LDU factorization of the approximation to ...