5 citations · 10 across the 10 of their papers we have counts for
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High degree quadrature rules with pseudorandom rational nodes
Mário M. Graça
After introducing the definitions of positive, negative and companion rules, from a given pair of companion rules we construct a new rule with higher degree of precision The scheme…
Four beautiful quadrature rules
Mário M. Graça
A framework is presented to compute approximations of an integral from a pair of companion rules and its associate rule. We show that an assoc…
Maps for global separation of roots
Mário M. Graça
Two simple predicates are adopted and certain real-valued piecewise continuous functions are constructed from them. This type of maps will be called quasi-step maps and aim to sepa…
Higher-order root distillers
Mário M. Graça
Recursive maps of high order of convergence (say or ) induce certain monotone step functions from which one can filter relevant information needed to globa…
Root Finding by High Order Iterative Methods Based on Quadratures
Mario M. Graça, Pedro M. Lima
We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed q…
Recursive families of higher order iterative maps
Mário M. Graça
To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence. These maps are based on model functions which can be written as…
Quadrature as a least-squares and minimax problem
Mário M. Graça
The vector of weights of an interpolatory quadrature rule with preassigned nodes is shown to be the least-squares solution of an overdetermined linear system here called {\…
A unified framework for the computation of polynomial quadrature weights and errors
Mário M. Graça, M. Esmeralda Sousa-Dias
For the class of polynomial quadrature rules we show that conveniently chosen bases allow to compute both the weights and the theoretical error expression of a -point rule via t…
A Simple Derivation of Newton-Cotes Formulas with Realistic Errors
Mário M. Graça
In order to approximate the integral , where is a sufficiently smooth function, models for quadrature rules are developed using a given {\it panel} of $n…
Double newtonisation of fixed point sequences
Mario M. Graca
A neutral fixed point of a real iteration map becomes a super attracting fixed point using a suitable double newtonisation. The map is so transformed into a map which i…