arXiv subjects

Simon Bossoney

Publications and source records attributed to Simon Bossoney.

3 recordsLinked to original sources

arXiv2026

A Direct Polynomial Approach to Spectral Decomposition

We give a direct construction of the spectral projectors of a complex square matrix, based on explicit interpolation polynomials previously introduced. This yields a spectral resolution $A=\sum_{i=1}^r(\lambda_iP_i+N_i)$ from which the Primary Decomposition Theorem, the Cayley--Hamilton theorem, criteria for diagonalizability, and the spectral theorem for normal matrices are proved by short formal arguments. A weaker form of the construction, extends to any perfect fields via a Galois invariance argument and produces the Jordan--Chevalley decomposition.

math.SP↗

arXiv2026

A Direct Approach to Hermite Interpolation

We introduce a family of polynomials satisfying the natural duality relations for Hermite interpolation, analogous to the classical Lagrange interpolation polynomials. They yield an explicit closed formula for the Hermite interpolant with arbitrary multiplicities, without recourse to divided differences, recursive corrections, or auxiliary B\'ezout identities. We also give a detailed account of Hermite's original approach to the problem, based on an integral formula, which he used both to derive the interpolating polynomial and to estimate the interpolation error for holomorphic data.

math.NA↗

arXiv2013

Volatility Swap Under the SABR Model

The SABR model is shortly presented and the volatility swap explained. The fair value for a volatility swap is then computed using the usual theory in financial mathematics. An analytical solution using confluent hypergeometric functions is found. The solution is then verified using Rama Cont's functional calculus.

q-fin.PR↗