J. M.
Reputation
424/400 score
 Mar 14 comment Is linear algebra laying the foundation for something important? @lisyarus, probably not "often", unless you deal with a lot of PDEs or networks. There's still much demand for dense methods, especially those that exploit structure. Nevertheless, linear algebra is one of the very handy tools in the box of a numericist. Mar 14 revised Integral of $\int\frac{dx}{(x^4-1)^{3/2}}$ added 1 character in body; edited title Mar 14 revised How to prove the result of this definite integral? added 3 characters in body; edited tags Mar 14 answered Solving $\ln{x}=\tan{x}$ with infinitely many solutions Mar 14 answered How to prove the result of this definite integral? Mar 14 answered Integral of $\int\frac{dx}{(x^4-1)^{3/2}}$ Mar 13 answered Circular Helicoid Mar 13 comment How to tell what dimension an object is? As a further complication, we have objects called "fractals" that feature a fractional dimension; the Koch snowflake has a dimension of $\approx 1.26186$, for instance. Mar 13 comment Algorithm(s) for computing an elementary symmetric polynomial @Thomas, a lower Hessenberg matrix like the one in this answer can be decomposed in $O(n^2)$ operations; the determinant is then easily obtained from the triangular factor. Have a look at "Hyman's method", for instance. Mar 12 revised Cauchy Principal value of integral with undefined point edited body Mar 11 revised Cauchy Principal value of integral with undefined point added 123 characters in body Mar 11 comment cubic root of negative numbers The last bit is the only blemish in an otherwise excellent answer. Mar 11 comment Cauchy Principal value of integral with undefined point Yes, if you perform the series expansion of that integrand at $z=0$, you should see something like $-\frac1{50}-\frac{16z^2}{1875}+\cdots$. Mar 11 revised Approximating hypergeometric function F(1,1+a,2+a,z) for z->1 edited tags Mar 11 comment Cauchy Principal value of integral with undefined point In principle, one could use a convergence acceleration method like Richardson extrapolation on the sequence generated in this manner, long as you pick an appropriate auxiliary sequence. Mar 11 answered Cauchy Principal value of integral with undefined point Mar 11 comment Cauchy Principal value of integral with undefined point NIntegrate[] can handle it directly: NIntegrate[1/((z + 1)^2 + 4) 1/(Exp[-z] - 1), {z, -∞, 0, ∞}, Method -> PrincipalValue] Mar 9 comment What is the intuitive relationship between SVD and PCA @sv_jan5, if memory serves, Golub/Van Loan mention the Läuchli example. A number of other numerical linear algebra books will have this discussion and similar examples; look around. Mar 8 comment What is the intuitive relationship between SVD and PCA @sv_jan, did ya even try the example I gave, if you have to ask that? Mar 6 comment Does anyone know a function that can describe a harmonic series? You'll want to look up the digamma function.