Zheng, N., Yin, J.F.: Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem. Numer. Algorithms 64(2), 245–262 (2013) Article MathSciNet MATH Google Scholar Zhou, P., Lu, C., Lin, Z., Zhang, C.: Tensor factorization for low-rank tensor compl...
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...
For commutingHermitianmatrices, there is a unitary matrixUthat jointly diagonalizes all matrices. For this significantly simpler situation, compared to the general non-Hermitian case, randomized methods based on (2) have recently been analyzed in [18], establishing favorable robustness and stability pr...
First, spatial audio synthesis between a sound-source and sound-field requires fast convolution algorithms between the audio-stream and the HRIRs. We introduce a novel sparse decomposition algorithm for HRIRs based on non-negative matrix factorization that allows for faster time-domain convolution ...
Numerical methods Numerical Aspects of CFD This section covers the numerical soul of CFD.
Matrix factorization algorithms QR (qr) LU (lu) Cholesky (chol) Arnoldi iteration (arnoldi) Eigenvalue algorithms QR (eigsQR) QR-Arnoldi (eigsArnoldi) Utilities : Vector and matrix norms, matrix condition number, Givens rotation, Householder reflection ...
(which has, in any case, to be done by LU factorization). Rare cases where is required are in statistics, where the diagonal elements of the inverse of the covariance matrix are relevant quantities, and in certain algorithms for computing matrix functions. ...
Traversing the contour in reverse order is equivalent to using another Vandermonde matrix as the transformation matrix. Our paper provides experimental results that show that this method does not work. The literature describes two algorithms that generalize the FFT on the unit circle: the Chirp ...
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...
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...