On the Differential and Full Algebraic Complexities of Operator Matrices Transformations

DOI10.1007/978-3-319-45641-6_1zbMath1453.34014OpenAlexW2513157961MaRDI QIDQ2829987

Sergey A. Abramov

Publication date: 9 November 2016

Published in: Computer Algebra in Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-45641-6_1

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Linear ordinary differential equations and systems (34A30) Complexity and performance of numerical algorithms (65Y20) Differential algebra (12H05)

Related Items (6)

Reducing triangular systems of ODEs with rational coefficients, with applications to coupled Regge-Wheeler equations ⋮ Matrices of scalar differential operators: divisibility and spaces of solutions ⋮ Revealing matrices of linear differential systems of arbitrary order ⋮ Package of procedures for inverting matrices whose entries are linear difference operators ⋮ Inverse linear difference operators ⋮ Explicit triangular decoupling of the separated Lichnerowicz tensor wave equation on Schwarzschild into scalar Regge-Wheeler equations

Cites Work

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• Computing the Hermite form of a matrix of Ore polynomials
• New effective differential Nullstellensatz
• Matrix multiplication via arithmetic progressions
• Remarks on the formulation of the Cauchy problem for general system of ordinary differential equations
• FFT-like multiplication of linear differential operators
• Essentially optimal computation of the inverse of generic polynomial matrices
• On simultaneous row and column reduction of higher-order linear differential systems
• On singular points of solutions of linear differential systems with polynomial coefficients
• Polynomial evaluation and interpolation on special sets of points
• Simple forms of higher-order linear differential systems and their applications in computing regular solutions
• Fraction-free row reduction of matrices of Ore polynomials.
• Gaussian elimination is not optimal
• Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients
• Certified dense linear system solving
• Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs
• On solutions of linear functional systems
• EG-eliminations
• On the Dimension of Solution Spaces of Full Rank Linear Differential Systems
• On Solution Spaces of Products of Linear Differential or Difference Operators
• Products of ordinary differential operators by evaluation and interpolation
• Multiplying matrices faster than coppersmith-winograd
• Integration in Finite Terms

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