Numerical linear algebra

Symbiosis between linear algebra and optimization(

The e ciency and e ectiveness of most optimization algorithms hinges on the numerical linear algebra algorithms that they utilize. E ective linear algebra is crucial to their success, and because of this, optimization applications have motivated fundamental advances in numerical linear algebra. This essay will highlight contributions of numerical linear algebra to optimization, as well as some ...

A 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...

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...

Some results on the block numerical range

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.

Umist Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra Departments of Mathematics Notes on Accuracy and Stability of Algorithms in Numerical Linear Algebra 1

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...