Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
SIAM Journal on Numerical Analysis
Approximate GCD and its application to ill-conditioned algebraic equations
ISCM '90 Proceedings of the International Symposium on Computation mathematics
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Approximate polynomial greatest common divisors and nearest singular polynomials
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
On the optimal stability of the Bernstein basis
Mathematics of Computation
Detection and validation of clusters of polynomial zeros
Journal of Symbolic Computation - Special issue: validated numerical methods and computer algebra
Optimization strategies for the approximate GCD problem
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On approximate GCDs of univariate polynomials
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
ACM Transactions on Mathematical Software (TOMS)
Solving Polynomials with Small Leading Coefficients
SIAM Journal on Matrix Analysis and Applications
Structured total least norm and approximate GCDs of inexact polynomials
Journal of Computational and Applied Mathematics
A unified approach to resultant matrices for Bernstein basis polynomials
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
The calculation of the degree of an approximate greatest common divisor of two polynomials
Journal of Computational and Applied Mathematics
GPGCD, an iterative method for calculating approximate GCD, for multiple univariate polynomials
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
A subdivision method for computing nearest gcd with certification
Theoretical Computer Science
IEEE Transactions on Signal Processing
QR factoring to compute the GCD of univariate approximate polynomials
IEEE Transactions on Signal Processing
The computation of multiple roots of a polynomial
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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The computation of the degree d of an approximate greatest common divisor of two Bernstein basis polynomials f(y) and g(y) that are noisy forms of, respectively, the exact polynomials f@?(y) and g@?(y) that have a non-constant common divisor is considered using the singular value decomposition of their Sylvester S(f,g) and Bezout B(f,g) resultant matrices. It is shown that the best estimate of d is obtained when S(f,g) is postmultiplied by a diagonal matrix Q that is derived from the vectors that lie in the null space of S(f,g), where the correct value of d is defined as the degree of the greatest common divisor of the exact polynomials f@?(y) and g@?(y). The computed value of d is improved further by preprocessing f(y) and g(y), and examples of the computation of d using S(f,g), S(f,g)Q and B(f,g) are presented.