nojka_kruva
  • Member for 10 years, 1 month
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Books for Numerical linear algebra
7 votes

My favorites are Matrix Computations by Golub and Van Loan and Numerical Linear Algebra by Trefethen and Bau. Together they cover all the important aspects of the field.

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F1 from ROC curve
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2 votes

The coordinates of points on the ROC curve are true positive rate (TPR) and false positive rate (TPR). These are given by: $$ TPR=TP/(TP+FN)$$ and $$ FPR=TP/(TP+FP)$$ The F1 score is given by: $$F_1=2*...

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Preconditioning of optimization problems
2 votes

The simplest example of an optimization problem which can be solved by casting it as a linear equation system is the linear least squares problem $$min_x||Ax-b||_2^2$$ By deriving this expression, we ...

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Modeling 2 conditionally dependent variables
1 votes

Since both variables are Gaussian, the natural model for their joint distribution is a multivariate Gaussian distribution.

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Gaussian Discriminant Analysis
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1 votes

I suggest that you'd start with learning some basic concepts in probability theory: continuous and discrete random variables, probability density functions, mean, variance and estimating them from a ...

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Submatrix with sum K
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1 votes

The trivial solution to this problem, which involves brute-forcing the sum of every possible submatrix is O(n^6), which consists of O(n^4) for iterating over all possible submatrices and another O(n^2)...

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Matrix-Square Root
1 votes

One way to deal with this problem is to approximate the solution by iterative methods. For example, by using Newton's method to solve the matrix equation $X^2-Y=0$. It leads to the following iteration:...

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solving a system of equation by rotation
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1 votes

It's called a Givens rotation. Similarly to Gaussian elimination, you can use a Givens rotation to eliminate a variable from a system of linear equations. The basic idea is to find a 2D rotation ...

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Generating Gauss-Seidel hard system
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0 votes

A matrix with a high condition number will do the trick. One way to construct such a matrix is to create a diagonal matrix with a huge first entry and a tiny last entry and multiply it from both ...

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Tools for plotting behavior of differential equations
0 votes

I'd use either MATLAB or Python for that. Both have strong visualization capabilities.

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