Lecture 8: Time discretization and some matrix algebra
ثبت نشده
چکیده
The goal of this lecture is to discuss more sophisticated time-marching schemes, and in particular, the major distinction between explicit and implicit methods.
منابع مشابه
Some results on Haar wavelets matrix through linear algebra
Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.
متن کاملMA 106 Linear Algebra lecture notes
8 Elementary operations and the rank of a matrix 25 8.1 Gauss transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 8.2 Elementary row operations . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.3 The augmented matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.4 Row reducing a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 8.5 Elem...
متن کاملRandomized Algorithms for Matrices and Data Lecture 1 - 09 / 04 / 2013 Lecture 1 : Introduction and Overview
This course will cover recent developments in randomized matrix algorithms of interest in large-scale machine learning and statistical data analysis applications. By this, we will mean basic algorithms for fundamental matrix problems—such as matrix multiplication, least-squares regression, lowrank matrix approximation, and so on—that use randomization in some nontrivial way. This area goes by t...
متن کاملSparse Matrix Algebra for Quantum Modeling of Large Systems
Matrices appearing in Hartree–Fock or density functional theory coming from discretization with help of atom–centered local basis sets become sparse when the separation between atoms exceeds some system–dependent threshold value. Efficient implementation of sparse matrix algebra is therefore essential in large–scale quantum calculations. We describe a unique combination of algorithms and data r...
متن کاملOn the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کامل