Computational Linear Algebra
نویسندگان
چکیده
Copyright: These notes may be reproduced provided the copies are not sold for profit. Contact the author at [email protected] for an up to date plain T E X source.
منابع مشابه
Classical Wavelet Transforms over Finite Fields
This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...
متن کاملA computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations
A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...
متن کاملClassical wavelet systems over finite fields
This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...
متن کاملInterval Linear Algebra and Computational Complexity
This work connects two mathematical fields – computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra – regularity and singularity, full column rank, solving a linear system, deciding solvability of a linear system, computing inverse matrix, eigenvalues, checking positive (semi)definiteness or stability. We discuss these problems and relati...
متن کاملAn Asynchronous API for Numerical Linear Algebra
We present a task-parallel asynchronous API for numerical linear algebra that utilizes multiple CPUs, multiple GPUs, or a combination of both. Furthermore, we present a wrapper of this interface for use in MATLAB. Our API imposes only small overheads, scales perfectly to two processor cores, and shows even better performance when utilizing computational resources on the GPU.
متن کاملRecent Progress in Linear Response Eigenvalue Problems
Linear response eigenvalue problems arise from the calculation of excitation states of many-particle systems in computational materials science. In this paper, from the point of view of numerical linear algebra and matrix computations, we review the progress of linear response eigenvalue problems in theory and algorithms since 2012.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001