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A ninth order polynomial interpolation (exact replication of the red curve at 10 points) In the mathematical field of numerical analysis , Runge's phenomenon ( German: [ˈʁʊŋə] ) is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced ...
A polynomial equation is solvable by radicals if its Galois group is a solvable group. In the case of irreducible quintics, the Galois group is a subgroup of the symmetric group S 5 of all permutations of a five element set, which is solvable if and only if it is a subgroup of the group F 5 , of order 20 , generated by the cyclic permutations ...
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
A Lozenge diagram is a diagram that is used to describe different interpolation formulas that can be constructed for a given data set. A line starting on the left edge and tracing across the diagram to the right can be used to represent an interpolation formula if the following rules are followed: [ 5 ]
Low-order polynomials tend to be smooth and high order polynomial curves tend to be "lumpy". To define this more precisely, the maximum number of inflection points possible in a polynomial curve is n-2, where n is the order of the polynomial equation. An inflection point is a location on the curve where it switches from a positive radius to ...
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Spoilers ahead! We've warned you. We mean it. Read no further until you really want some clues or you've completely given up and want the answers ASAP. Get ready for all of today's NYT ...
Ars Magica is a role-playing game set in 'Mythic Europe' – a historically grounded version of Europe and the Levant around AD 1200, with the added conceit that conceptions of the world prevalent in folklore and institutions of the High Middle Ages are factual reality (a situation known informally as the "medieval paradigm").