14 papers
Analogue of the Cauchy-Schwarz inequality for determinants: a simple proof
Avram Sidi
In this note, we present a simple proof of an analogue of the Cauchy-Schwarz inequality relevant to products of determinants. Specifically, we show that $$ |\det(A^*MB)|^2\leq \det…
Application of a Generalized Secant Method to Nonlinear Equations with Complex Roots
Avram Sidi
The secant method is a very effective numerical procedure used for solving nonlinear equations of the form . In a recent work [A. Sidi, Generalization of the secant method…
PVTSI$^{\boldmath(m)}$: A Novel Approach to Computation of Hadamard Finite Parts of Nonperiodic Singular Integrals
Avram Sidi
We consider the numerical computation of $I[f]=\intBar^b_a f(x)\,dx$, the Hadamard Finite Part of the finite-range singular integral , with…
Exactness and Convergence Properties of Some Recent Numerical Quadrature Formulas for Supersingular Integrals of Periodic Functions
Avram Sidi
In a recent work, we developed three new compact numerical quadrature formulas for finite-range periodic supersingular integrals $I[f]=\intBar^b_a f(x)\,dx$, where $f(x)=g(x)/(x-t)…
Unified Compact Numerical Quadrature Formulas for Hadamard Finite Parts of Singular Integrals of Periodic Functions
Avram Sidi
We consider the numerical computation of finite-range singular integrals $$I[f]=\intBar^b_a f(x)\,dx,\quad f(x)=\frac{g(x)}{(x-t)^m},\quad m=1,2,\ldots,\quad a<t<b,$$ that are defi…
Generalization of the Secant Method for Nonlinear Equations (extended version)
Avram Sidi
The secant method is a very effective numerical procedure used for solving nonlinear equations of the form . It is derived via a linear interpolation procedure and employs…
A Convergence Study for Reduced Rank Extrapolation on Nonlinear Systems
Avram Sidi
Reduced Rank Extrapolation (RRE) is a polynomial type method used to accelerate the convergence of sequences of vectors . It is applied successfully in differ…
A New Algorithm for the Higher-Order -Transformation
Avram Sidi
Let the scalars be defined via the linear equations Here the and are known and the…
A de Montessus Type Convergence Study for a Vector-Valued Rational Interpolation Procedure of Epsilon Class
Avram Sidi
In a series of recent publications of the author, three interpolation procedures, denoted IMPE, IMMPE, and ITEA, were proposed for vector-valued functions , where $F : \C \to…
Acceleration of Convergence of Some Infinite Sequences Whose Asymptotic Expansions Involve Fractional Powers of via the transformation
Avram Sidi
In this paper, we discuss the application of the author's transformation to accelerate the convergence of infinite series when the terms $a…
On a Vectorized Version of a Generalized Richardson Extrapolation Process
Avram Sidi
Let $\{\xx_m\}$ be a vector sequence that satisfies $$ \xx_m\sim \sss+\sum^\infty_{i=1}α_i \gg_i(m)\quad\text{as $m\to\infty$},$$ $\sss$ being the limit or antilimit of $\{\xx_m\}$…
A Further Property of Functions in Class
Avram Sidi
We say that a function belongs to the set if it has an asymptotic expansion of the form as , which can be…
SVD-MPE: An SVD-Based Vector Extrapolation Method of Polynomial Type
Avram Sidi
An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors $\{\xx_m\}$, where $\xx_m\in \C^N$, being…
Minimal Polynomial and Reduced Rank Extrapolation Methods Are Related
Avram Sidi
Minimal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are two polynomial methods used for accelerating the convergence of sequences of vectors . Th…