The nearest polynomial to multiple given polynomials with a given zero in the real case

Given multiple univariate or multivariate real polynomials f 1 , … , f n and a desired real zero z, we investigate a problem of finding the nearest polynomial f ˜ to f 1 , … , f n having z as a zero. We use a pair of norms to define the nearest polynomial. We remark that the difficulty of the problem depends on the norm pairs and give computing methods when the norm pairs consist of the p-norm and the q-norm for ( p , q ) = ( 2 , 2 ) , ( 2 , ∞ ) , and ( ∞ , ∞ ) .