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An Introduction to Pseudo-Linear Algebra (1996)
| Content Provider | CiteSeerX |
|---|---|
| Author | Bronstein, Manuel Petkovsek, Marko |
| Abstract | Pseudo-linear algebra is the study of common properties of linear differential and difference operators. We introduce in this paper its basic objects (pseudo-derivations, skew polynomials, and pseudo-linear operators) and describe several recent algorithms on them, which, when applied in the differential and difference cases, yield algorithms for uncoupling and solving systems of linear differential and difference equations in closed form. Introduction Linear ordinary differential equations are equations of the form a n (t) d n y(t) dt n + : : : + a 1 (t) dy(t) dt + a 0 (t)y(t) = b(t) (1) or systems of the form d dt 2 6 4 y 1 (t) . . . y n (t) 3 7 5 = A(t) 2 6 4 y 1 (t) . . . y n (t) 3 7 5 +B(t) (2) while linear ordinary difference equations are equations of the form a n (t)y(t + n) + : : : + a 1 (t)y(t + 1) + a 0 (t)y(t) = b(t) (3) or systems of the form 2 6 4 y 1 (t + 1) . . . y n (t + 1) 3 7 5 = A(t) 2 6 4 y 1 (t) . . . y n (t) 3 7 5 +B(t) (4) where in both... |
| File Format | |
| Volume Number | 157 |
| Journal | Theoretical Computer Science |
| Language | English |
| Publisher Date | 1996-01-01 |
| Access Restriction | Open |
| Subject Keyword | Pseudo-linear Algebra Describe Several Recent Algorithm Difference Equation Basic Object Difference Case Introduction Linear Ordinary Differential Equation Skew Polynomial Difference Operator Closed Form Pseudo-linear Operator Yield Algorithm Linear Ordinary Difference Equation Common Property |
| Content Type | Text |
| Resource Type | Article |
