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Algorithms for computer algebra
TLDR
This book discusses Polynomials GCD Computation, the construction of bases for Polynomial Ideals, and the Risch Integration Algorithm, which automates the process of solving Systems of Equation.
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Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance
Many nonlinear option pricing problems can be formulated as optimal control problems, leading to Hamilton-Jacobi-Bellman (HJB) or Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations. We show that such…
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A penalty method for American options with jump diffusion processes
TLDR
An implicit discretization method is developed for pricing such American options where the underlying asset follows a jump diffusion process and sufficient conditions for global convergence of the discrete penalized equations at each timestep are derived.
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A Semi-Lagrangian Approach for American Asian Options under Jump Diffusion
TLDR
A semi-Lagrangian method is presented to price continuously observed fixed strike Asian options and it is observed that the nonsmoothness at the strike in the payoff affects the convergence rate; a subquadratic convergence rate is observed.
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A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
TLDR
A recurrence relation is presented for the computation of a basis for the corresponding linear solution space of these approximants, and these methods result in fast (and superfast) reliable algorithms for the inversion of stripedHankel, layered Hankel, and (rectangular) block-Hankel matrices.
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Fraction-free row reduction of matrices of Ore polynomials
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A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets
TLDR
A fast, incremental parsing algorithm is developed, motivated by the two-dimensional structure of written mathematics, and a correction mechanism is developed that allows users to navigate parse results and choose the correct interpretation in case of recognition errors or ambiguity.
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Computer Algebra
TLDR
This introduction gives a working definition of computer algebra, the organization of research activities in this field, and the overall structure and the intention of the present volume on computer algebra.
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Asymptotically fast computation of Hermite normal forms of integer matrices
This paper presents a new algorithm for computing the Hermite normal form H of an A Z n m of rank m to gether with a unimodular pre multiplier matrix U such that UA H Our algorithm requires O m nM m…
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Grammar-based techniques for creating ground-truthed sketch corpora
TLDR
A general approach to creating large, ground-truthed corpora for structured sketch domains such as mathematics, where random sketch templates are generated automatically using a grammar model of the sketch domain, and annotated with ground-truth.
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