Claude-Pierre Jeannerod

Essentially optimal computation of the inverse of generic polynomial matrices

We present an inversion algorithm for nonsingular n × n matrices whose entries are degree d polynomials over a field. The algorithm is deterministic and, when n is a power of two, requires O ∼ (n3d) field operations for a generic input; the soft-O notation O∼ indicates some missing log(nd) factors. Up to such logarithmic factors, this asymptotic complexity is of the same order as the number of distinct field elements necessary to represent the inverse matrix.

Improved Error Bounds for Inner Products in Floating-Point Arithmetic

Given two floating-point vectors

Rank-profile revealing Gaussian elimination and the CUP matrix decomposition

x,y

A floating-point library for integer processors

of dimension

Faster Algorithms for Multivariate Interpolation With Multiplicities and Simultaneous Polynomial Approximations

n

Asymptotically fast polynomial matrix algorithms for multivariable systems

and assuming rounding to nearest, we show that if no underflow or overflow occurs, any evaluation order for an inner product returns a floating-point number

On relative errors of floating-point operations: Optimal bounds and applications

{\widehat r}

Fast Computation of Minimal Interpolation Bases in Popov Form for Arbitrary Shifts

such that

Improved backward error bounds for LU and Cholesky factorizations

|{\widehat r}- x^Ty| \leqslant nu|x|^T|y|

Solving toeplitz- and vandermonde-like linear systems with large displacement rank

with